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    "# Getting started with PyMC4: Bayesian neural networks\n",
    "\n",
    "This article demonstrates how to implement a simple Bayesian neural network for regression with an early [PyMC4 development snapshot](https://github.com/pymc-devs/pymc4/tree/1c5e23825271fc2ff0c701b9224573212f56a534) (from Jul 29, 2020). It can be installed with \n",
    "\n",
    "```bash\n",
    "pip install git+https://github.com/pymc-devs/pymc4@1c5e23825271fc2ff0c701b9224573212f56a534\n",
    "```\n",
    "\n",
    "I'll update this article from time to time to cover new features or to fix breaking API changes. The latest update (Aug. 19, 2020) includes the recently added support for variational inference (VI). The following sections assume that you have a basic familiarity with [PyMC3](https://docs.pymc.io/). If this is not the case I recommend reading [Getting started with PyMC3](https://docs.pymc.io/notebooks/getting_started.html) first."
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      "4.0a2\n",
      "2.4.0-dev20200818\n",
      "0.12.0-dev20200818\n"
     ]
    }
   ],
   "source": [
    "import logging\n",
    "import pymc4 as pm\n",
    "import numpy as np\n",
    "import arviz as az\n",
    "\n",
    "import tensorflow as tf\n",
    "import tensorflow_probability as tfp\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "print(pm.__version__)\n",
    "print(tf.__version__)\n",
    "print(tfp.__version__)\n",
    "\n",
    "# Mute Tensorflow warnings ...\n",
    "logging.getLogger('tensorflow').setLevel(logging.ERROR)"
   ]
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   "source": [
    "## Introduction to PyMC4\n",
    "\n",
    "PyMC4 uses [Tensorflow Probability](https://www.tensorflow.org/probability) (TFP) as backend and PyMC4 random variables are wrappers around TFP distributions. Models must be defined as [generator](https://docs.python.org/3/glossary.html#term-generator) functions, using a `yield` keyword for each random variable. PyMC4 uses [coroutines](https://www.python.org/dev/peps/pep-0342/) to interact with the generator to get access to these variables. Depending on the context, PyMC4 may sample values from random variables, compute log probabilities of observed values, ... and so on. Details are covered in the [PyMC4 design guide](https://github.com/pymc-devs/pymc4/blob/master/notebooks/pymc4_design_guide.ipynb). Model generator functions must be decorated with ` @pm.model` as shown in the following trivial example:"
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    "@pm.model\n",
    "def model(x):\n",
    "    # prior for the mean of a normal distribution\n",
    "    loc = yield pm.Normal('loc', loc=0, scale=10)\n",
    "    \n",
    "    # likelihood of observed data\n",
    "    obs = yield pm.Normal('obs', loc=loc, scale=1, observed=x)"
   ]
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   "source": [
    "This models normally distributed data centered at a location `loc` to be inferred. Inference can be started with `pm.sample()` which uses the [No-U-Turn Sampler](https://jmlr.org/papers/volume15/hoffman14a/hoffman14a.pdf) (NUTS). Samplers other than NUTS are currently not implemented in PyMC4."
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   "execution_count": 3,
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       "Attributes:\n",
       "    created_at:     2020-08-19T12:02:26.831730\n",
       "    arviz_version:  0.9.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-760aba9f-e8e0-419d-8d81-8e71af20154e' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-760aba9f-e8e0-419d-8d81-8e71af20154e' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 10</li><li><span class='xr-has-index'>draw</span>: 1000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-22ce4953-7d4d-4677-88fb-f0fd3dfa3bf5' class='xr-section-summary-in' type='checkbox'  checked><label for='section-22ce4953-7d4d-4677-88fb-f0fd3dfa3bf5' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 7 8 9</div><input id='attrs-1cf94adc-9d59-4ca6-a9ec-9fbc331d1dca' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-1cf94adc-9d59-4ca6-a9ec-9fbc331d1dca' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-0e895be2-a098-44da-bf78-9983c53aad15' class='xr-var-data-in' type='checkbox'><label for='data-0e895be2-a098-44da-bf78-9983c53aad15' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 995 996 997 998 999</div><input id='attrs-cf4ff1a3-1a3e-4c79-b0ec-b27f0cb6f89c' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-cf4ff1a3-1a3e-4c79-b0ec-b27f0cb6f89c' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ec2a889f-724a-484c-a1cf-b798a1c13925' class='xr-var-data-in' type='checkbox'><label for='data-ec2a889f-724a-484c-a1cf-b798a1c13925' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 997, 998, 999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-2f534014-5d9d-4f37-89be-56f20432daa4' class='xr-section-summary-in' type='checkbox'  checked><label for='section-2f534014-5d9d-4f37-89be-56f20432daa4' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>model/loc</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>3.1448023 3.1448023 ... 3.4603796</div><input id='attrs-6e5bdc67-6445-4461-bb8b-b53063e942dd' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-6e5bdc67-6445-4461-bb8b-b53063e942dd' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-f0500855-f670-4a94-9ccb-de33a6309a99' class='xr-var-data-in' type='checkbox'><label for='data-f0500855-f670-4a94-9ccb-de33a6309a99' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[3.1448023, 3.1448023, 3.1593454, ..., 3.1752453, 3.5500278,\n",
       "        3.3998082],\n",
       "       [3.096355 , 2.9651537, 3.107913 , ..., 2.7815466, 3.302857 ,\n",
       "        3.3626337],\n",
       "       [3.0079126, 3.2646103, 3.2475855, ..., 3.3154554, 3.2643337,\n",
       "        3.132182 ],\n",
       "       ...,\n",
       "       [3.213623 , 3.1980019, 3.1980019, ..., 2.8879852, 3.052567 ,\n",
       "        3.4903805],\n",
       "       [3.198672 , 3.4714966, 2.9759057, ..., 3.3256674, 3.007779 ,\n",
       "        3.007779 ],\n",
       "       [2.835832 , 2.8538866, 2.8538866, ..., 3.075596 , 3.004984 ,\n",
       "        3.4603796]], dtype=float32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-e5584752-b506-441e-b895-61bcedd0603d' class='xr-section-summary-in' type='checkbox'  checked><label for='section-e5584752-b506-441e-b895-61bcedd0603d' class='xr-section-summary' >Attributes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2020-08-19T12:02:26.831730</dd><dt><span>arviz_version :</span></dt><dd>0.9.0</dd></dl></div></li></ul></div></div><br></div>\n",
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       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:           (chain: 10, draw: 1000)\n",
       "Coordinates:\n",
       "  * chain             (chain) int64 0 1 2 3 4 5 6 7 8 9\n",
       "  * draw              (draw) int64 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999\n",
       "Data variables:\n",
       "    lp                (chain, draw) float32 -43.887486 -43.887486 ... -45.533813\n",
       "    tree_size         (chain, draw) int32 3 1 1 1 1 1 1 1 1 ... 3 1 3 1 1 3 1 3\n",
       "    diverging         (chain, draw) bool False False False ... False False False\n",
       "    energy            (chain, draw) float32 -44.09497 -44.962246 ... -47.662434\n",
       "    mean_tree_accept  (chain, draw) float32 -0.11299977 ... -1.8010322\n",
       "Attributes:\n",
       "    created_at:     2020-08-19T12:02:26.832872\n",
       "    arviz_version:  0.9.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-fd5ed5ec-e673-4430-94fa-3dbe68b0c585' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-fd5ed5ec-e673-4430-94fa-3dbe68b0c585' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 10</li><li><span class='xr-has-index'>draw</span>: 1000</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-efe08ce7-c145-4230-b123-d2b4961eae2c' class='xr-section-summary-in' type='checkbox'  checked><label for='section-efe08ce7-c145-4230-b123-d2b4961eae2c' class='xr-section-summary' >Coordinates: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 7 8 9</div><input id='attrs-3e8d2da3-c723-4aa9-b317-ccfb3dba5203' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3e8d2da3-c723-4aa9-b317-ccfb3dba5203' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-d5997943-6a3d-4c82-b69a-90e270b12d51' class='xr-var-data-in' type='checkbox'><label for='data-d5997943-6a3d-4c82-b69a-90e270b12d51' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 995 996 997 998 999</div><input id='attrs-3c4cb427-50a3-4d0d-acb8-25f13c474a3e' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-3c4cb427-50a3-4d0d-acb8-25f13c474a3e' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-7ba3ca33-d381-4d62-a581-7c43f7b30ab8' class='xr-var-data-in' type='checkbox'><label for='data-7ba3ca33-d381-4d62-a581-7c43f7b30ab8' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 997, 998, 999])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-c6bc2890-9da1-48ec-b2a6-8f8038e1861e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-c6bc2890-9da1-48ec-b2a6-8f8038e1861e' class='xr-section-summary' >Data variables: <span>(5)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>lp</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-43.887486 ... -45.533813</div><input id='attrs-65086520-ad77-4779-9f70-5c3afa02c708' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-65086520-ad77-4779-9f70-5c3afa02c708' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-c25c6bb7-14bd-4ccb-8f82-9ec477426ecf' class='xr-var-data-in' type='checkbox'><label for='data-c25c6bb7-14bd-4ccb-8f82-9ec477426ecf' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-43.887486, -43.887486, -43.897667, ..., -43.916054, -46.54659 ,\n",
       "        -44.98605 ],\n",
       "       [-43.899372, -44.28523 , -43.890137, ..., -45.69251 , -44.33845 ,\n",
       "        -44.7044  ],\n",
       "       [-44.10273 , -44.16057 , -44.095512, ..., -44.40666 , -44.159447,\n",
       "        -43.883797],\n",
       "       ...,\n",
       "       [-43.9917  , -43.955574, -43.955574, ..., -44.75345 , -43.970715,\n",
       "        -45.84589 ],\n",
       "       [-43.956974, -45.6463  , -44.234173, ..., -44.465443, -44.103218,\n",
       "        -44.103218],\n",
       "       [-45.17109 , -45.017273, -45.017273, ..., -43.926025, -44.113483,\n",
       "        -45.533813]], dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>tree_size</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>int32</div><div class='xr-var-preview xr-preview'>3 1 1 1 1 1 1 1 ... 3 1 3 1 1 3 1 3</div><input id='attrs-ee92ccec-4846-4e0b-9408-db05d6fe8bac' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-ee92ccec-4846-4e0b-9408-db05d6fe8bac' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-25e10c78-9899-49ac-b381-7d593afdee38' class='xr-var-data-in' type='checkbox'><label for='data-25e10c78-9899-49ac-b381-7d593afdee38' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[3, 1, 1, ..., 1, 1, 1],\n",
       "       [1, 3, 1, ..., 3, 3, 3],\n",
       "       [3, 3, 1, ..., 1, 1, 1],\n",
       "       ...,\n",
       "       [1, 1, 1, ..., 1, 1, 3],\n",
       "       [3, 1, 3, ..., 3, 3, 3],\n",
       "       [1, 1, 3, ..., 3, 1, 3]], dtype=int32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>diverging</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>bool</div><div class='xr-var-preview xr-preview'>False False False ... False False</div><input id='attrs-486fc9cb-893a-489c-b8e8-e9632100a900' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-486fc9cb-893a-489c-b8e8-e9632100a900' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-8b07e58c-a82a-43dc-a680-dbf7ce2fe013' class='xr-var-data-in' type='checkbox'><label for='data-8b07e58c-a82a-43dc-a680-dbf7ce2fe013' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       ...,\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False],\n",
       "       [False, False, False, ..., False, False, False]])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>energy</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-44.09497 -44.962246 ... -47.662434</div><input id='attrs-49be9485-0bc6-45f0-86d7-a5b0d5faa673' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-49be9485-0bc6-45f0-86d7-a5b0d5faa673' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-90202480-a63a-4a48-ac76-07be9c6c87e3' class='xr-var-data-in' type='checkbox'><label for='data-90202480-a63a-4a48-ac76-07be9c6c87e3' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-44.09497 , -44.962246, -43.90053 , ..., -47.178867, -46.633278,\n",
       "        -46.38453 ],\n",
       "       [-44.1807  , -44.30795 , -44.069817, ..., -45.740902, -44.99158 ,\n",
       "        -44.736084],\n",
       "       [-44.36696 , -44.163994, -44.251163, ..., -44.76689 , -44.440952,\n",
       "        -44.003162],\n",
       "       ...,\n",
       "       [-44.87733 , -44.015293, -45.389606, ..., -44.754826, -44.384026,\n",
       "        -45.847645],\n",
       "       [-44.192295, -45.749332, -46.55621 , ..., -47.500885, -44.505745,\n",
       "        -44.819065],\n",
       "       [-46.209038, -45.75422 , -47.55198 , ..., -44.166405, -44.148354,\n",
       "        -47.662434]], dtype=float32)</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span>mean_tree_accept</span></div><div class='xr-var-dims'>(chain, draw)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>-0.11299977 ... -1.8010322</div><input id='attrs-012becec-39c8-4f4a-928a-09466c8d3b44' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-012becec-39c8-4f4a-928a-09466c8d3b44' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-ea710169-f2c8-46a9-90e6-b31cdd947b64' class='xr-var-data-in' type='checkbox'><label for='data-ea710169-f2c8-46a9-90e6-b31cdd947b64' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[-0.11299977, -1.4377098 , -0.00593183, ..., -4.5058823 ,\n",
       "        -1.5323563 ,  0.        ],\n",
       "       [ 0.        , -0.17513256,  0.        , ..., -0.24506885,\n",
       "        -0.03921076, -0.09310422],\n",
       "       [-0.01966013, -0.0111048 ,  0.        , ...,  0.        ,\n",
       "         0.        ,  0.        ],\n",
       "       ...,\n",
       "       [ 0.        ,  0.        , -1.9999924 , ..., -0.50117874,\n",
       "         0.        , -0.5668998 ],\n",
       "       [ 0.        , -0.9840775 , -0.8787381 , ..., -0.9555875 ,\n",
       "        -0.13321258, -0.63191855],\n",
       "       [ 0.        ,  0.        , -1.033627  , ..., -0.13674697,\n",
       "        -0.10919955, -1.8010322 ]], dtype=float32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-1a28bcab-5e86-4e52-a5a0-452f0b573782' class='xr-section-summary-in' type='checkbox'  checked><label for='section-1a28bcab-5e86-4e52-a5a0-452f0b573782' class='xr-section-summary' >Attributes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2020-08-19T12:02:26.832872</dd><dt><span>arviz_version :</span></dt><dd>0.9.0</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "            <li class = \"xr-section-item\">\n",
       "                  <input id=\"idata_observed_data58c78130-9067-4274-9a10-d836cc6f426d\" class=\"xr-section-summary-in\" type=\"checkbox\">\n",
       "                  <label for=\"idata_observed_data58c78130-9067-4274-9a10-d836cc6f426d\" class = \"xr-section-summary\">observed_data</label>\n",
       "                  <div class=\"xr-section-inline-details\"></div>\n",
       "                  <div class=\"xr-section-details\">\n",
       "                      <ul id=\"xr-dataset-coord-list\" class=\"xr-var-list\">\n",
       "                          <div style=\"padding-left:2rem;\"><div><svg style=\"position: absolute; width: 0; height: 0; overflow: hidden\">\n",
       "<defs>\n",
       "<symbol id=\"icon-database\" viewBox=\"0 0 32 32\">\n",
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       "</svg>\n",
       "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
       " *\n",
       " */\n",
       "\n",
       ":root {\n",
       "  --xr-font-color0: var(--jp-content-font-color0, rgba(0, 0, 0, 1));\n",
       "  --xr-font-color2: var(--jp-content-font-color2, rgba(0, 0, 0, 0.54));\n",
       "  --xr-font-color3: var(--jp-content-font-color3, rgba(0, 0, 0, 0.38));\n",
       "  --xr-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --xr-disabled-color: var(--jp-layout-color3, #bdbdbd);\n",
       "  --xr-background-color: var(--jp-layout-color0, white);\n",
       "  --xr-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --xr-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
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       "\n",
       "html[theme=dark],\n",
       "body.vscode-dark {\n",
       "  --xr-font-color0: rgba(255, 255, 255, 1);\n",
       "  --xr-font-color2: rgba(255, 255, 255, 0.54);\n",
       "  --xr-font-color3: rgba(255, 255, 255, 0.38);\n",
       "  --xr-border-color: #1F1F1F;\n",
       "  --xr-disabled-color: #515151;\n",
       "  --xr-background-color: #111111;\n",
       "  --xr-background-color-row-even: #111111;\n",
       "  --xr-background-color-row-odd: #313131;\n",
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       "\n",
       ".xr-wrap {\n",
       "  display: block;\n",
       "  min-width: 300px;\n",
       "  max-width: 700px;\n",
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       "\n",
       ".xr-text-repr-fallback {\n",
       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
       "  display: none;\n",
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       "\n",
       ".xr-header {\n",
       "  padding-top: 6px;\n",
       "  padding-bottom: 6px;\n",
       "  margin-bottom: 4px;\n",
       "  border-bottom: solid 1px var(--xr-border-color);\n",
       "}\n",
       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
       "  display: inline;\n",
       "  margin-top: 0;\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-obj-type {\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-sections {\n",
       "  padding-left: 0 !important;\n",
       "  display: grid;\n",
       "  grid-template-columns: 150px auto auto 1fr 20px 20px;\n",
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       "\n",
       ".xr-section-item {\n",
       "  display: contents;\n",
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       "\n",
       ".xr-section-item input {\n",
       "  display: none;\n",
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       "\n",
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       "\n",
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       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
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       "\n",
       ".xr-section-summary {\n",
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       "\n",
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       "\n",
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       "\n",
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       "  font-size: 11px;\n",
       "  width: 15px;\n",
       "  text-align: center;\n",
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       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
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       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
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       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
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       "\n",
       ".xr-section-inline-details {\n",
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       "\n",
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       "\n",
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       "\n",
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       "  grid-column: 1 / -1;\n",
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       "  grid-template-columns: 20px auto;\n",
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       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
       "}\n",
       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
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       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
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       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt, dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:          (model/obs_dim_0: 30)\n",
       "Coordinates:\n",
       "  * model/obs_dim_0  (model/obs_dim_0) int64 0 1 2 3 4 5 6 ... 24 25 26 27 28 29\n",
       "Data variables:\n",
       "    model/obs        (model/obs_dim_0) float64 5.034 3.825 3.969 ... 3.918 2.585\n",
       "Attributes:\n",
       "    created_at:     2020-08-19T12:02:26.834054\n",
       "    arviz_version:  0.9.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-4a0bed98-4a81-4d50-898f-8b341589b37c' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-4a0bed98-4a81-4d50-898f-8b341589b37c' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>model/obs_dim_0</span>: 30</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-ab618cc8-9501-4ded-a471-3864367ee1ce' class='xr-section-summary-in' type='checkbox'  checked><label for='section-ab618cc8-9501-4ded-a471-3864367ee1ce' class='xr-section-summary' >Coordinates: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>model/obs_dim_0</span></div><div class='xr-var-dims'>(model/obs_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 ... 24 25 26 27 28 29</div><input id='attrs-d128c28b-80ec-4592-8d29-148a133b82c0' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d128c28b-80ec-4592-8d29-148a133b82c0' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-247a41d4-9a55-4b83-838d-e5b6ac58c687' class='xr-var-data-in' type='checkbox'><label for='data-247a41d4-9a55-4b83-838d-e5b6ac58c687' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,\n",
       "       18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-337b60ad-7777-481e-9204-e9fa74d53adb' class='xr-section-summary-in' type='checkbox'  checked><label for='section-337b60ad-7777-481e-9204-e9fa74d53adb' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>model/obs</span></div><div class='xr-var-dims'>(model/obs_dim_0)</div><div class='xr-var-dtype'>float64</div><div class='xr-var-preview xr-preview'>5.034 3.825 3.969 ... 3.918 2.585</div><input id='attrs-f9f9f980-47ed-4002-a77b-ef0cd804f510' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-f9f9f980-47ed-4002-a77b-ef0cd804f510' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-27f1f456-d201-4121-b106-dbc67024918e' class='xr-var-data-in' type='checkbox'><label for='data-27f1f456-d201-4121-b106-dbc67024918e' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([5.03434655, 3.82462505, 3.96940926, 2.3396569 , 3.5108133 ,\n",
       "       3.0514346 , 2.10080958, 1.43897365, 3.36524396, 2.54937186,\n",
       "       3.00850969, 2.11411964, 3.51740442, 3.3991824 , 3.80398466,\n",
       "       4.44110725, 1.68463182, 3.92476337, 2.57933469, 4.36729299,\n",
       "       1.57571855, 4.29665483, 3.78128164, 2.11619165, 2.56151748,\n",
       "       2.68069589, 2.30618091, 4.04778368, 3.91752526, 2.58532026])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-5c7e92f4-7141-4c9b-ae4b-730859d0a34e' class='xr-section-summary-in' type='checkbox'  checked><label for='section-5c7e92f4-7141-4c9b-ae4b-730859d0a34e' class='xr-section-summary' >Attributes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2020-08-19T12:02:26.834054</dd><dt><span>arviz_version :</span></dt><dd>0.9.0</dd></dl></div></li></ul></div></div><br></div>\n",
       "                      </ul>\n",
       "                  </div>\n",
       "            </li>\n",
       "            \n",
       "              </ul>\n",
       "            </div>\n",
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       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       ".xr-wrap{width:700px!important;} </style>"
      ],
      "text/plain": [
       "Inference data with groups:\n",
       "\t> posterior\n",
       "\t> sample_stats\n",
       "\t> observed_data"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 30 data points normally distributed around 3\n",
    "x = np.random.randn(30) + 3\n",
    "\n",
    "# Inference\n",
    "trace = pm.sample(model(x))\n",
    "trace"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The returned `trace` object is an ArviZ [`InferenceData`](https://arviz-devs.github.io/arviz/notebooks/XarrayforArviZ.html) object. It contains posterior samples, observed data and sampler statistics. The posterior distribution over `loc` can be displayed with:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(trace, var_names=['model/loc']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A recent addition to PyMC4 is variational inference and supported methods currently are `advi` and `fullrank_advi`. After fitting the model, posterior samples can be obtained from the resulting `approximation` object (representing a mean-field approximation in this case)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "fit = pm.fit(model(x), num_steps=10000, method='advi')\n",
    "trace = fit.approximation.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(trace, var_names=['model/loc']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The history of the variational lower bound  (= negative loss) during training can be displayed with"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(-fit.losses)\n",
    "plt.ylabel('Variational lower bound')\n",
    "plt.xlabel('Step');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which confirms a good convergence after about 10,000 steps. Models can also be composed through nesting and used like other PyMC4 random variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "@pm.model\n",
    "def prior(name, loc=0, scale=10):\n",
    "    loc = yield pm.Normal(name, loc=loc, scale=scale)\n",
    "    return loc\n",
    "\n",
    "@pm.model\n",
    "def model(x):\n",
    "    loc = yield prior('loc')\n",
    "    obs = yield pm.Normal('obs', loc=loc, scale=1, observed=x)\n",
    "    \n",
    "trace = pm.sample(model(x))\n",
    "az.plot_posterior(trace, var_names=['model/prior/loc']);    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A more elaborate example is shown below where a neural network is composed of several layers. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The dataset used in the following example contains `N` noisy samples from a sinusoidal function `f` in two distinct regions (`x1` and `x2`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x, noise):\n",
    "    \"\"\"Generates noisy samples from a sinusoidal function at x.\"\"\"\n",
    "    return np.sin(2 * np.pi * x) + np.random.randn(*x.shape) * noise\n",
    "\n",
    "N = 40\n",
    "noise = 0.1\n",
    "\n",
    "x1 = np.linspace(-0.6, -0.15, N // 2, dtype=np.float32)\n",
    "x2 = np.linspace(0.15, 0.6, N // 2, dtype=np.float32)\n",
    "\n",
    "x = np.concatenate([x1, x2]).reshape(-1, 1)\n",
    "y = f(x, noise=noise)\n",
    "\n",
    "x_test = np.linspace(-1.5, 1.5, 200, dtype=np.float32).reshape(-1, 1)\n",
    "f_test = f(x_test, noise=0.0)\n",
    "\n",
    "plt.scatter(x, y, marker='o', c='k', label='Samples')\n",
    "plt.plot(x_test, f_test, 'k--', label='f')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian neural network\n",
    "\n",
    "### Model definition\n",
    "\n",
    "To model the non-linear relationship between `x` and `y` in the dataset we use a ReLU neural network with two hidden layers, 5 neurons each. The weights of the neural network are random variables instead of deterministic variables. This is what makes a neural network a Bayesian neural network. Here, we assume that the weights are independent random variables. \n",
    "\n",
    "The neural network defines a prior over the mean `loc` of the data likelihood `obs` which is represented by a normal distribution. For simplicity, the aleatoric uncertainty (`noise`) in the data is assumed to be known. Thanks to PyMC4's model composition support, priors can be defined layer-wise using the `layer` generator function and composed to a neural network as shown in function `model`. During inference, a posterior distribution over the neural network weights is obtained. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "@pm.model\n",
    "def layer(name, x, n_in, n_out, prior_scale, activation=tf.identity):\n",
    "    w = yield pm.Normal(name=f'{name}_w', loc=0, scale=prior_scale, batch_stack=(n_in, n_out))\n",
    "    b = yield pm.Normal(name=f'{name}_b', loc=0, scale=prior_scale, batch_stack=(1, n_out))\n",
    "    \n",
    "    return activation(tf.tensordot(x, w, axes=[1, 0]) + b)\n",
    "\n",
    "@pm.model\n",
    "def model(x, y, prior_scale=1.0):    \n",
    "    o1 = yield layer('l1', x, n_in=1, n_out=5, prior_scale=prior_scale, activation=tf.nn.relu)\n",
    "    o2 = yield layer('l2', o1, n_in=5, n_out=5, prior_scale=prior_scale, activation=tf.nn.relu)\n",
    "    o3 = yield layer('l3', o2, n_in=5, n_out=1, prior_scale=prior_scale)\n",
    "    \n",
    "    yield pm.Normal(name='obs', loc=o3, scale=noise, observed=y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `batch_stack` parameter of random variable constructors is used to define the shape of the random variable.\n",
    "\n",
    "### Inference\n",
    "\n",
    "Tensorflow will automatically run inference on a GPU if available. With the current version of PyMC4, MCMC inference using NUTS on a GPU is quite slow compared to a multi-core CPU (need to investigate that in more detail). To enforce inference on a CPU set environment variable `CUDA_VISIBLE_DEVICES` to an empty value. There is no progress bar visible yet during sampling but the following shouldn't take longer than a few minutes on a modern multi-core CPU."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# MCMC inference with NUTS\n",
    "trace = pm.sample(model(x, y, prior_scale=3), burn_in=100, num_samples=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variational inference is significantly faster but the results are less convincing than the MCMC results. I need to investigate that further to see if I'm doing something wrong or if this is an issue with the current PyMC4 development snapshot. We'll therefore use the MCMC results in the following section. If you want to see the VI results, run the following cell instead of the previous one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Variational inference with full rank ADVI\n",
    "fit = pm.fit(model(x, y, prior_scale=0.5), num_steps=150000, method='fullrank_advi')\n",
    "\n",
    "# Draw samples from the resulting mean-field approximation\n",
    "trace = fit.approximation.sample(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The full `trace` can be visualized with `az.plot_trace(trace)`. Here, we only display the posterior over the last layer weights (without bias)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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T9PHHH0uSPl63V+OzEvX3e+5ScnKyli9frkmTJikyMlKjR4/W3LlzfbK/H3zwgWbNmqXg4O+v382ePVs7duzQmjVrNH1Qqlbkl6qosu6o60pKSpIk1dfX7zd90aJFevXVV3X33Xd7N3gAANrJ2+395+sLFBrk0LH9k4/Y3jeZM2eOV9v71NhwDeoZo7ff+0CSNGvWrOb30tLSNHXqVH3wwQdtWmdQUJDi4+MPatcBAACAroREO+BDeXl5uvXWW3XnnXfqn//8p7799ltddtllmj17tmbPnq3XXntNjY2Nmj17tizLkiRdc801uvPOO3XZZZfpvffe0znnnKNLLrlE7777bvN6c3NzdeaZZ+q5557T66+/rilTpujUU0/V6+9/qg17KnSSpzd7dXW1fvazn+nyyy/X66+/rrCwMM2aNUvV1dXN63K5XGpsbDziw+l0HnE/q6qqlJ+fr0GDBu03ffDgwZKkDRs2aMagVFmW9NV3+w65DqfTqbq6Oq1YsUJ33nmnZs2apZ49v++Vb1mWrrnmGv3ud79TWlrnlsUBAOBIvNnev/LG25rUL0lRYcGHbe/nzZu33/a93d5PzUnWdxs3Kq1PH0VHR++3rcGDB2vDhg1H/Uwsy1JjY6OKior0wAMPaNOmTbrkkksOmm/GjBkKCgpSVlaW7rzzzqMecwAAAAD+itIxgA8VFxdr/vz56tevnyRp1apVuueee/Tss88234ZtWZZOP/10bdiwQSEhIXrsscf0r3/9Sz/72c8kSSeeeKJ2796t22+/XWeccYYk6eqrr27ehsvl0vTp07V27Vo98MgT0vCLddKQHnr6U3eN1AcffFAzZsyQJPXq1UujR4/W119/rVNOOUWSdMkllxzUY/5Axx9/vL788svDvl9aWipJio+P3296QkKCJKmkpETDescpOTpMX2zcp1lj+hy0jqFDh2rjxo2SpJNPPlnPPffcfu//61//0t69e/Xb3/72iLECANDZvNXeb9qWr/c++Jeu//lsSYdv759++mkdc8wxze95u70/dkCK/lpdoZCI6IPmSUhIUElJyVE/k1deeUU/+tGPJElRUVF65ZVXNGHChOb34+LidOONN+rYY49VaGio3n33Xd12223at2+fHnrooaOuHwAAAPA3JNoBH8rKymo+6ZaknJwcSWo+EW45befOndqyZYscDofOOeccNTY2Ns9zwgkn6KWXXpLT6VRQUJB27Nihm2++WZ9++ql2797d3Dsuqd8IjT8pVumJkZKk0NBQTZs2rXk9Q4YMkSTt2LGjedqcOXP2O5E/lJiYmOafnU5n8/Yk7Vcq5kgcDqNpA1P08do9anS6FBy0/w01r7/+usrKyrR69WrdcccdOu+88/Tuu+/KGKOysjLddNNN+sc//qGIiIhWbQ8AgM7irfY+ecBY1b/2qqbmuEuoHa69b5lkl7zf3k/ISpTDYVRV13jE+Y/k5JNP1uLFi1VYWKgXXnhBs2fP1vvvv98c5+jRozV69Ojm+U888USFhYXp/vvv1x//+EclJye3e9sAAACAHUi0Az50YA/v0NDQg6Y3TautrVVhYaGcTqfi4uIOub7du3erd+/eOuuss1RRUaE77rhDOTk5ioqK0o0336K5q7bopCHfD54WExMjh+P7hHbLbTXJyMhQnz4H9zBvyRjT/HO/fv20ffv25te5ublKSXEPnFZWVrbfck093pp6ts8YlKrXlu7QsrxSTcjef5DToUOHSpKmTJmiwYMH6/jjj9cXX3yhGTNm6K677lJGRoZOOumk5t7zjY2NamhoUGlpqWJiYhQUFHTEfQAAwFe83d6H1ZfJ5Yo+ZHt/6623qqCgYL/5vd3eR4QGKa1HsnLzVh40T0lJSXO7fiQJCQkaN26cJPdgqLt27dKtt96qr7/++rDLnHvuufrb3/6mVatW7XeRAgAAAAgEJNoBP5KYmKjg4GDNmzdvvxPmJqmpqdq8ebOWL1+uDz74oPl2cEnaXVQuSTppaI+DljuStpaOeeedd1RX9/2Apr1791ZoaKjS09MPqtna9LqpdvvU/skKdhh9vqHgoER7S2PGjJEkbd26VTNmzNDGjRu1ZMmSQ57YJyQkaO7cuZo6derRdxYAAD9wqPa+0enShU8t1DE5yerRo8dh2/uampp2bbOt7f24kcO0/uOXtHV3kfr2SmqeZ8OGDQeNydIao0eP1ssvv3zEeZoS/S0v8AMAAACBgkQ74EdmzJghp9OpsrIyzZw585DzNJ1gh4WFNU/bvn27NqxYrIiefTWkV2ybttnW0jHDhw8/5Dynnnqq3nzzTd15553NvctfeeUVpaena9iwYZKk2PAQjctK0Nff7dONpx7+JL1pkLfs7GxJ0p133qnf/OY3+83zm9/8RnFxcbr99tsPGxMAAP7oUO390u0lakzap/NOHa3Q0NDDtvfz5s3TiBEj2rzNtrb3PzvvLD13z8168KkX9Pc//kqStGvXLs2dO1ePPvpom7ZtWZbmz5/f3K4fzmuvvabg4OB27R8AAABgNxLtgB8ZOHCgrrjiCs2ePVu/+93vNG7cONXW1mrt2rX67rvv9NRTT2nQoEHq06ePrr/+ev3pT39SRUWFbr3tNgXFJCkmPLjNvcCysrKUlZXV4dhvuOEGvfDCC7rooot06aWXavHixXriiSf02GOP7RfTf688VjFTZqvo5xOUFB2miy66SAMGDNCoUaMUGRmpZcuW6W9/+5smT56s6dOnS1Jzor6l+Ph4JScn71eTFgCAQHCo9v6VBVtUvnC+Xtnzus749zOHbO9vu+02paWltWubbW3vp48ZrKSxp+jJe27T+KwEpaSkaM6cOcrMzNSFF17YPN8dd9yhO+64o7nW/Ny5c3X//ffrnHPOUUZGhoqKivTss89qwYIFeuedd5qXu/LKK5WSkqLx48crNDRU77//vh5++GH95je/UVJS0kHxAAAAAP6ORDvgZx555BENGDBATz75pG699VbFxsZqyJAh+vnPfy7J3bPtjTfe0FVXXaVzzz1Xffr00QWX/loPPveWYlz7bIs7JydHH374oa677jqdeuqp6tmzp+677z794he/2G8+l8spWS59u6VIZ47srQkTJujf//637r33XjmdTmVnZ+tXv/qVrr322kOWzwEAoCs4sL1XaKSie2Rq5v9dJ+nQ7f3NN9+sL7/8UmvWrPF5fA6H0axf3qJ3n75P1113naqrq3X88cfrpZdeUnh4ePN8LpdLTqez+XV6erqCgoL0hz/8Qfv27VNKSopGjRqlb775RpMnT26eb/DgwXrqqaf0wAMPqL6+Xjk5Obrvvvv061//2uf7BgAAAPiCsSzLm+vz6soAtM5f3l+vZ+blavmtJyk6zL+vnzldlkbd8bFOH95Ld/+QW8MBL/FGQWPacMAmlXWNGnX7x/rFsX2PWFqtsz377Tbd9r+1mvu76UpPjLQ7HKCrYlACAAC6CLqLAl3Alxv3aVxmot8n2SUpyGE0pV+S5m4qlJcv9AEAEJAW5Rap0WXp2P7Jdoeyn8n93CVc5m8tsjkSAAAAwP+RaAcC3K7SGm3cW6Hpg1LsDqXVpuYka2dpjfKKq+0OBQAA283fUqTQIIfGZibYHcp++qdGKzEqVAtItAMAAABHRaIdCHBfbnTXZZ82MNXmSFrvmBx3j71vNhfaHAkAAPZbmFusURnxCg8JsjuU/RhjNKlvohZsKeIuNAAAAOAoSLQDAe6r7wrUOy5c/VOj7Q6l1bKTo9Q7LlzzSLQDALq58toGrdlZpkl9k+wO5ZAm903SrrJa5RfX2B0KAAAA4NdItAMBzOmyNH9Lkab2T5YxgTOOkjFGU3KS9e2WIrlc9JADAHRfS7eVyGVJk7IT7Q7lkJouAFA+BgAAADgyEu1AAFu7q0zltY3NpVgCycTsRJVWN2jzvkq7QwEAwDYLtrrrs4/O8K/67E1yUqOVHE2ddgAAAOBoSLQDAWzeZvdJ7+R+/nm7+ZFMzHbHvDC32OZIAACwz4KtRRqVHq+IUP+qz97EGKPxWYlavJ32GgAAADgSEu1AAPt2S6EG9IhWaky43aG0WXpihHrEhmkRiXYAQDdVUdugNbvKNbGvf5aNaTIuK1H5xTXaU1ZrdygAAACA3yLRDgSoukanFm8r1pR+gVc2RnL3kJuQnaTFucWyLOq0AwC6nyXbS+R0WX47EGqT8VnusjaLt3FxHAAAADgcEu1AgFq2vVS1Da6ArM/eZEJ2ovaU1yq/uMbuUAAA6HQLtxYrJMhojJ/WZ28ypFesIkODtIREOwAAAHBYJNqBAPXtlkI5jPz+dvMjmZDljn0RJ+4AgG5oybZiDUuL89v67E2CgxwanRGvxdtK7A4FAAAA8Fsk2oEANW9zoUb0iVdseIjdobRb/9RoxUeGaFFukd2hAADQqWobnFq1o0zjswLjgvm4zERt2FOu8toGu0MBAAAA/BKJdiAAVdQ2aOWOMh2T4981XY/G4TAal5nIgKgAgG5nzc4y1TtdGpfp32VjmozPSpTLkpbnldodCgAAAOCXSLQDAWhRbrGcLkvHBOhAqC1NzE7UtqJqFZTX2h0KAACdpqkMy9gASbSPyohXkMNQpx0AAAA4DBLtQACat7lIYcEOjQmQk/MjmZBNnXYAQPezZFux+qVEKSk6zO5QWiU6LFhDesVqMe01AAAAcEgk2oEANG9zocZnJSo8xL8HT2uNob1jFRkaRPkYAEC34XJZWrK9JGDqszcZl5WgFfmlqm902R0KAAAA4HdItAMBZl9FnTburdCUAK/P3iQ4yKGxmQkk2gEA3cbmfZUqq2nQuABLtE/ISlRtg0trd5XZHQoAAADgd0i0AwHm2y2FktQl6rM3mZCVqI17K1RaXW93KAAA+FxT+ZXxWYFVAm6sJ94lnvryAAAAAL5Hoh0IMN9uLlJseLCGpcXZHYrXjM9OlGVx4g4A6B6WbCtRSkyYMhIj7Q6lTVJjwpWVFEmddgAAAOAQSLQDAWbelkJN6pukIIexOxSvGZUer9AgByfuAIBuYVleicZkxMuYwGvLx2Ulasn2ElmWZXcoAAAAgF8h0Q4EkB0l1dpRUqMp/bpGffYm4SFBGpkep4XUaQcAdHGFlXXaXlStMRmBVTamyfisBBVX1WtrYZXdoQAAAAB+hUQ7EEAWbnUnoif27VqJdkkan5WoNTvLVF3faHcoAAD4zPK8UknSmMzATLQ3DeC6hLvQAAAAgP2QaAcCyKLcYsVFhGhgjxi7Q/G6CdmJanRZzQkIAAC6ouV5JQp2GA0P0LFW+iZHKTEqVItyGVcFAAAAaIlEOxBAFuYWaXxWohxdqD57k9EZCTJGWrqdE3cAQNe1LK9EQ3rHKjwkyO5Q2sUYo3GZCVqynR7tAAAAQEsk2oEAsbe8VtuKqjWpb6LdofhEXESIBqTGkGgHAHRZjU6XVuaXBWx99ibjsxK1vahaBRW1docCAAAA+A0S7UCAaBoodEJ210y0S+56tcvySuRyWXaHAgCA123cW6GaBqdGZ8TbHUqHjM1yXyhYuo2L4wAAAEATEu1AgFi4tUjRYcEa0ivW7lB8ZlxmgipqG7V5X6XdoQAA4HXLmgZCDfAe7cN6xyks2KEl3IUGAAAANCPRDgSIRbnFGpeVoOCgrvvPdmymO/GwhB5yAIAuaPn2EiVHh6lPQoTdoXRIaLBDI9PjtWQbddoBAACAJl03Ywd0IUWVddpUUNmly8ZIUmZSpJKiQqnTDgDokpbnl2pMRryMCfxBzcdlJmjtrnLV1DvtDgUAAADwCyTagQCw2NNjbGJ2ks2R+JYxprlOOwAAXUlxVb1yC6s0OsDLxjQZl5WgRpelFfmldocCAAAA+AUS7UAAWLC1WOEhDg1Pi7M7FJ8bm5mg3MIqFVXW2R0KAABes9xzEXlMgA+E2qSpzjzlYwAAAAA3Eu1AAFiUW6yxmQkKDe76/2Sb6rQ3DRgHAEBXsDyvVEEOoxF94u0OxSviI0M1oEc0A6ICAAAAHl0/awcEuLLqBq3fU64JWV27bEyT4WlxCgky1GkHAHQpy/JKNLhXjCJCg+wOxWvGZiZqWV6JnC7L7lAAAAAA25FoB/zcku3FsixpYt+uPRBqk/CQIA3tHadlJNoBAF2E02VpZX5pc7mVrmJcZoIqahv13d4Ku0MBAAAAbEeiHfBzC3OLFRrk0Kj0eLtD6TTjMhO0ckep6htddocCAECHfbe3QlX1zi6XaB+f5e4EQPkYAAAAgEQ74PcWbi3SqPR4hYd0nVvNj2ZsZoLqGl1at7vc7lAAAOiwZZ6BUEd3kYFQm6QnRiglJkxLGRAVAAAAINEO+LPKukat2VWuCdndo2xMkzGeAVGp0w4A6AqWbS9VUlSoMhIj7Q7Fq4wxGpeZQI92AAAAQCTaAb+2dLt7gLHuUp+9SY/YcPVJiNDS7fSQAwAEvuV5JRqdES9jjN2heN24rETtKKnRnrJau0MBAAAAbEWiHfBji3KLFOQwXa6ma2uMzUzQ0u0lsizL7lAAAGi30up6bS2s0ugu2paP89yFtoSL4wAAAOjmSLQDfmzh1mINT4tTVFiw3aF0urGZCdpbXqedpTV2hwIAQLstzy+VpC570XxI71hFhARpyTbKxwAAAKB7I9EO+KnaBqdW7ijVxG5Wn71JU0KCOu0AgEC2PK9UDiON6BNndyg+ERLk0Mj0OHq0AwAAoNsj0Q74qWV5JWpwdr/67E0G9YxRZGiQlpFoBwAEsOV5JRrYM7ZL3502PitR63dXqKqu0e5QAAAAANuQaAf81KLcYhkjjc3snon24CCHRqXHa2keiXYAQGByuSytyC/V6Ix4u0PxqbGZCXJ69hUAAADorki0A35q4dZiDekVq7iIELtDsc24zAR6yAEAAtbWwkpV1DZqdHq83aH41JjMBBkjLd5G+RgAAAB0XyTaAT9U3+jSsrwSTeim9dmbjPH0kFu5o9TuUAAAaLNleaWSpNFddCDUJrHhIRrYI4ZxVQAAANCtkWgH/NCqHaWqa3RpYnaS3aHYqikxQZ12AEAgWp5XqtjwYPVNjrI7FJ8bl5WgZdtL1Oh02R0KAAAAYAsS7YAfWpjrvvW6u/doj4sI0YAe0fSQAwAEpOV5JRqVkSCHw9gdis+Ny0xUVb1TG/ZU2B0KAAAAYAsS7YAfWphbrAE9opUYFWp3KLYbm5mgpdtL5HJZdocCAECrVdY16ru9FV2+PnuTsZnuu9C4OA4AAIDuikQ74GcanC4t2VasSX27d9mYJmMyElRe26gt+yrtDgUAgFZbtaNULksanRFvdyidok9ChHrGhmsJiXYAAAB0UyTaAT+zZmeZquud3b4+exN6yAEAAtFyz0Coo7pJj3ZjjMZmJWjJtmK7QwEAAABsQaId8DMLtrpPUCf27d712ZtkJ0cpITKERDsAIKAszytR35QoxUd2nzJw4zITtLusVjtLa+wOBQAAAOh0JNoBP7Mwt0g5qdFKjg6zOxS/YIxx12nPI9EOAAgMlmVpeV6pRqcn2B1Kpxqf5e4kQK92AAAAdEck2gE/0uh0aXFusSbRm30/YzMTtXVflYqr6u0OBQCAo8ovrlFRVX23qc/eZFDPGEWFBmkxiXYAAAB0QyTaAT+ydle5qqjPfpCmOu3L6dUOAAgAy/Pd7VV3S7QHBzk0NitRC7eSaAcAAED3Q6Id8CMLthZJoj77gUb0iVOww1CnHQAQEJbnlSoiJEgDe8TYHUqnm9Q3UZsKKlVYWWd3KAAAAECnItEO+JGFucXqmxKl1Jhwu0PxK+EhQRqaFkeiHQAQEJbnlbgvEgd1v0PtyX3dd+U1dR4AAAAAuovud/QP+Cmny/LUZ6dszKGMzUjQyh2lanC67A4FAIDDqm1wau2uco3O6F4DoTYZlhanqNAgzd9Coh0AAADdC4l2wE+s21WuirpGTcymbMyhjM1MUG2DS+t2ldsdCgAAh7V2V5kaXVa3q8/eJCTIofHZifRoBwAAQLdDoh3wE00npPRoP7QxmfGSRPkYAIBfW55XKkkanR5vaxx2mtw3SVv2VamgvNbuUAAAAIBOQ6Id8BMLc4uUnRylHrHUZz+UXnERSouP0NI8Eu0AAP+1PK9UafERSu3G7XlTp4EFucU2RwIAAAB0HhLtgB9wuiwtzC3WpL6UjTmSsZkJWkaPdgCAH1ueV6Ixmd2zPnuTob1jFRMWTJ12AAAAdCsk2gE/sH53uSpqGzUxm7IxRzI2M0G7y2q1q7TG7lAAADjInrJa7Sqr7dZlYyQpOMihCdmJWkiddgAAAHQjJNoBP9BUn30iPdqPaKynhyB12gEA/mhFvrt96q4DobY0qW+SthZWaS912gEAANBNkGgH/MDC3GJlJkWqV1yE3aH4tUE9YxQREkSiHQDgl5bnlSo0yKEhvWPtDsV2k/t56rTTqx0AAADdBIl2wGZOl6VFucWaRNmYowoOcmhUeryWMSAqAMAPLc8r1dC0WIUFB9kdiu0G94pVbDh12gEAANB9kGgHbLZuV7nKaho0qR9lY1pjbGaC1u4qV3V9o92hAADQrMHp0qqdpRqd3r0HQm0S5DCakJ2k+fRoBwAAQDdBoh2w2bwthZKkY3KSbY4kMIzNTJDTZWllfpndoQAA0GzjngrVNrioz97C5H5J2l5UzSDmAAAA6BZItAM2m7e5UAN7xCg1JtzuUAJCUwKD8jEAAH+yPI+BUA80yTPIO3XaAQAA0B2QaAdsVNvg1KLcYk3JoT57a8VHhionNZoBUQEAfmVZXqmSo8OUFs/A5k0G94xVXEQIiXYAAAB0CyTaARst216iukaXplI2pk3GZSZoWV6JXC7L7lAAAJAkLdlerHGZCTLG2B2K33A4jCZmJ1KnHQAAAN0CiXbARvO2FCrIYTSxLz3a22JMZoJKqxu0tbDS7lAAANCeslrlF9doXBYDoR7omJxk5RfXKK+o2u5QAAAAAJ8i0Q7Y6JvNRRqdHq/osGC7Qwko47PcNV8X5VI+BgBgvyXbiyV93z7he8f2d9+199WmfTZHAgAAAPgWiXbAJmXVDVq9o1RTKBvTZllJkeoRG0bNVwCAX1iyrUQRIUEa0jvW7lD8TnZylNLiIzT3OxLtAAAA6NpItAM2mb+1SC5L1GdvB2OMJvVN0oKtRbIs6rQDAOy1eFuxxmTGKySIQ+sDGWN03IAUfbulSA1Ol93hAAAAAD7D2QBgk2+3FCoyNEij0uPtDiUgTeqbpIKKOuUWVtkdCgCgG6uobdD63eUal0nZmMM5rn+yKusatSK/1O5QAAAAAJ8h0Q7Y5JvNhZqYnajQYP4ZtsckzwCyC7YW2xwJAKA7W5ZXKpdFffYjmZKTLIeRvqZ8DAAAALowMnyADXaV1mjrviodQ9mYdstKilRqDHXaAQD2WrKtWEEOo1EZ8XaH4rfiIkI0Kj1eX28qtDsUAAAAwGdItAM2mLfZfaJJor39qNMOAPAHi7cVa0ivWEWHBdsdil87bkCKVu0oVUlVvd2hAAAAAD5Boh2wwbdbipQcHaqBPWLsDiWgUacdAGCn+kaXVuSXalxWgt2h+L3jBqTIsqSvN1E+BgAAAF0TiXagk1mWpW82F2pKv2Q5HMbucALapL7uerjUaQcA2GHtrjLVNrioz94KI/vEKykqVJ9vKLA7FAAAAMAnSLQDnWxTQaX2VdRpKmVjOiw7OYo67QAA2yzZViJJGpdJj/ajCXIYTRuYqi837lOj02V3OAAAAIDXkWgHOtnX37lvmZ6Sk2RzJIGPOu0AADst3laszKRIpcaG2x1KQDhhcKrKahq0LK/U7lAAAAAAryPRDnSyr77bp5zUaPVJiLQ7lC6BOu0AADtYlqUl20s0LpOyMa01tX+ygh2G8jEAAADokki0A52our5RC7cWa9qAFLtD6TKo0w4AsMPWwioVV9VrQjZlY1orNjxEE7IT9fmGvXaHAgAAAHgdiXagE83fUqR6p0vTBqbaHUqXQZ12AIAdlmxzX+Adx0CobTJjUKq+21up/OJqu0MBAAAAvIpEO9CJvty4T5GhQRpP7zevoU47AMAOi7eVKDEqVH2To+wOJaCcMLiHJOmz9fRqBwAAQNdCoh3oJJZl6YuNBZrSL0lhwUF2h9OlUKcdANDZlmwr1rjMBBlj7A4loGQnRyknNVofrSXRDgAAgK6FRDvQSbbsq9KOkhodT9kYr6NOOwCgMxWU12pbUbXGUzamXU4Z2lOLthWrpKre7lAAAAAAryHRDnSSLzcWSBIDofpAU532b7cU2h0KAKAbmO8ZF2RS3ySbIwlMJw/tKafL0qeUjwEAAEAXQqId6CSfbyhQTmq00hMj7Q6lyzHGaGpOsr7dUiSXizrtAADfWrC1SDHhwRrSO9buUALSsLRYpcVH6KO1e+wOBQAAAPAaEu1AJyiradCi3GKd6BkADN43tX+yiqvqtW53ud2hAAC6uPlbijQxO1FBDuqzt4cxRjOH9NDXmwpVVddodzgAAACAV5BoBzrBV9/tU6PL0swh1Gf3lak5yZKkuZsoHwMA8J3dZTXaVlRN2ZgOOnloT9U3uvTVd/vsDgUAAADwChLtQCf4bP1eJUaFalR6gt2hdFmpseEa1DNGczdxwg4A8J0Fnvrsk/uRaO+I8VkJSowK1furd9sdCgAAAOAVJNoBH2twuvTFhgLNGJTKLeY+dmz/ZC3ZVqKaeqfdoQAAuqj5W4oUFxGiwT2pz94RwUEOnTqspz5bX6DqesrHAAAAIPCRaAd8bMm2EpXXNurEwZSN8bVj+6eo3unSwtwiu0MBAHRRC7YWa2J2ohxcPO+wM0f2Vk2DU5+uL7A7FAAAAKDDSLQDPvbZ+r0KDXLo2P4pdofS5U3ITlRosEPfUKcdAOADO0trlFdcTdkYLxmflagesWF6Z+Uuu0MBAAAAOoxEO+BDlmXp43V7NSUnSVFhwXaH0+WFhwRpQlaivqZOOwDAB+Ztdl/IJdHuHUEOozNG9NZXG/eprKbB7nAAAACADiHRDvjQut3lyiuu1ilDe9odSrcxbWCKvttbqZ2lNXaHAgDoYr7ZVKiUmDAN7BFjdyhdxpkje6ve6dLHa/fYHQoAAADQISTaAR/6cM0eOYw0c0gPu0PpNqYNdNfC/2ID9V4BAN7jclmat7lQU3OSZQz12b1lZJ84pSdG6H+UjwEAAECAI9EO+NCHa/ZoQnaikqLD7A6l2+iXEqX0xAh9uZFEOwDAe9bvKVdRVb2m5iTbHUqXYozR2aPSNG9zofaU1dodDgAAANBuJNoBH9lcUKlNBZU6dVgvu0PpVowxmjEwVfM2F6m2wWl3OACALqJpoO2p/Um0e9usMX3ksqQ3l++0OxQAAACg3Ui0Az7y4ZrdkqSTqc/e6aYNSlVNg1MLc4vtDgUA0EV8s7lQ/VOj1SM23O5Qupzs5CiNzUzQG8t2yLIsu8MBAAAA2oVEO+AjH6zZo9EZ8eoZxwl5Z5vcN0nhIQ7qtAMAvKK2walFucX0ZvehWWPStKmgUqt3ltkdCgAAANAuJNoBH8gtrNLaXeU6jbIxtggPCdKUfsn6YmMBPeMAAB22ZFuJ6hpdOpZEu8+cMaK3QoMden3pDrtDAQAAANqFRDvgA/9bsUvGSGeMJNFul+mDUrW9qFpb9lXaHQoAIMB9vWmfQoKMJmYn2R1KlxUXEaKZQ3ro7ZW7VNfIGCsAAAAIPCTaAS+zLEtvr9ypidmJ6hUXYXc43daJg1MlSR+t3WtzJACAQPfFhgJNyE5UVFiw3aF0aReMS1dpdQNtNwAAAAISiXbAy9buKtfWfVX6wag0u0Pp1nrFRWhEnzh9so6TdQBA++0oqdamgkpNH5hqdyhd3tScZKUnRujFhdvtDgUAAABoMxLtgJe9vWKnQoKMTh3W0+5Qur2ThvTQivxSFZTX2h0KACBAfblxnyRpGol2n3M4jGaPz9CCrcXaSuk3AAAABBgS7YAXuVyW3lm5W8cPSFF8ZKjd4XR7M4e4L3Z8sp5e7QCA9vlyY4HSEyPULyXK7lC6hfPG9VGww+jlxfl2hwIAAAC0CYl2wIsWbC3SnvJanUXZGL8woEe0MhIjKR8DAGiXukan5m0u0rQBqTLG2B1Ot5AaE64TB/fQa0t3MCgqAAAAAgqJdsCL/rt0h2LCg3XSkB52hwJJxhidNKSHvt1cpIraBrvDAQAEmEW5xappcGr6oBS7Q+lWfjIpQ8VV9Xpv1W67QwEAAABajUQ74CXltQ36YM1unTWyt8JDguwOBx4nDe2peqdLn28osDsUAECA+WLDPoUGOzS5b7LdoXQrU3OS1S8lSv+at02WZdkdDgAAANAqJNoBL3l35W7VNrh03rh0u0NBC+MyE5QaE6b3V9MrDgDQepZl6ZP1ezSlX5IiQrmA3pmMMbr4mGyt3lmmZXmldocDAAAAtAqJdsBL/rs0XwN6RGtknzi7Q0ELDofRqcN66suN+1RZ12h3OACAALFxb4Xyi2t08tCedofSLc0anaaY8GD9+9ttdocCAAAAtAqJdsALNhdUanleqc4bm37UwdLeeustjRgxQmFhYcrOztb9999/xPmvvfZaGWP029/+dr/pGzZs0MSJExUXF6fZs2ersrJyv/e//vprpaWlHTT9UP7973/LGHPIeefMmaPk5O9vmd+2bZuMMc2PqKgo9evXTz/5yU80d+7cg5a/+OKLNW7cuKPG4Eunj+itukaXPlvPoKgAgNb5eO1eGSOdMDjV59vi2OBgUWHBumBcuj5YvVt7ymqPGi8AAABgNxLtgBe8uDBPIUFGZ49OO+J88+bN06xZszRhwgS98847uuSSS/T73/9eDz744CHnX7dunZ5++mnFxsYe9N7FF1+snJwcvfrqq1q3bp3uuuuu5vdcLpd+/etf6y9/+Yuio6M7tG+Hc++992r+/Pl6//339cc//lFFRUU67rjjdPvtt/tkex1B+RgAQFt9sm6vRqfHKzUm3Kfb4djg8H42JUsuy9K/vs31cqQAAACA9wXbHQAQ6KrrG/Xfpfk6dVgvpcSEHXHeO+64Q8ccc4yeeuopSdJJJ52k0tJS3XHHHfrlL3+p0NDQ/ea/5ppr9Otf/1rPPffcftMrKyu1cOFCvfPOO0pJSVFpaanuvffe5hPqZ555RiEhIbrooou8uKf7GzhwoCZNmiRJOv7443XxxRfr1ltv1Zw5c3T88cdr2rRpPtt2WzWVj3l5cb4q6xoVHcafPgDA4e0qrdHqnWW68dRBPt8WxwaHl54YqdNH9NYLC/L0y2k5iosI8UHUAAAAgHfQox3ooP+t2KWK2kZdNDnzqPOuWLFCM2fO3G/aSSedpJKSEs2fP3+/6a+99po2bNigG2+88aD11NfXS5IiIiIkSZGRkc3TysvLdcstt+ihhx46ahkbb7vtttvUu3dvPf7445263dagfAwAoLU+9bQVM4f08Pm2ODY4siuO76vKukY9v2C7lyMDAAAAvItEO9ABlmXpP/O3a1DPGI3LTDjq/LW1tQf1TGt6vX79+uZpNTU1uv7663X33XcrKirqoPUkJiYqKytL//jHP1RcXKx//vOfzbVO//SnP+nEE0/U5MmT27w/TqdTjY2N+z1cLlerlw8KCtKMGTO0YMGCNm/b18ZlJqhXXLjeXrHL7lAAAH7u47V71S8lSv1SfFNipSWODY5saO84HT8gRf+at021Dc52rQMAAADoDNRPADpgWV6p1u0u15/PGdaqHmI5OTlavHjxftMWLVokSSouLm6e9pe//EW9evXShRdeeNh1PfroozrvvPP0hz/8Qf3799cjjzyizZs366mnntLq1avbtT/x8fGHnJ6UlNTqdfTp00d79/pfr3GHw+gHo9L05NytKqysU3L0kcv8AAC6p+Kqes3fWqTLj+vbKdvj2ODorji+n3705AL9d+kOXTTp6HcQAgAAAHagRzvQAf/+dptiwoJ19qgjD4La5IorrtBbb72lJ598UiUlJfroo490//33S5IcDvc/x9zcXN17771Hvb371FNPVUFBgTZu3Kj169crIyND1113na699lr16dNHjzzyiDIyMpSRkaFHH320VfF9/fXXWrx48X6PSy+9tFXLNrEsq03zd6ZzRqfJ6bL07kp6tQMADu2jtXvkdFk6fUSvTtkexwZHN6lvosZkxOuxLzarrpFe7QAAAPBP9GgH2im/uFrvr96tn0/NVlQrB9e85JJLtHLlSl155ZW67LLLFBkZqb/+9a+65ppr1LNnT0nSjTfeqFNPPVUDBw5UaWmpJMnlcqmurk6lpaWKi4trPsmOjIzUgAEDJEmffPKJVq5cqVdeeUUrV67UH//4R3377beSpMmTJ2vq1KkaMWLEEeMbPXq0oqP3v03+3XffbfVnIkk7d+5Ujx6+r2nbHgN7xmhwr1i9uWKXLj4m2+5wAAB+6P3Vu5WVFKkhvWI7ZXscGxydMUbXzhygi55epFcX5+uiyVntXhcAAADgK/RoB9rp6W9yZST93zFZrV4mKChIDz/8sPbt26dVq1Zp7969mjRpkiQ1P2/cuFFvvPGGEhISmh/5+fl6+OGHlZCQoJ07dx60XqfTqWuvvVZ/+9vfFBERoS+//FIzZszQoEGDNGjQIJ1wwgn66quvvLHbR9TY2KjPP/+8XTVgO8us0WlamV+qLfsq7Q4FAOBniqvq9e2WIp02vFenDRrKsUHrTM1J1rjMBD3yxRZqtQMAAMAv0aMdaIfS6nq9uiRfZ43qrV5xEW1evukkWXLXU50yZYoGDRokSXrqqadUWbl/Enj27Nk6/vjjdeWVVyolJeWg9T322GNKSEjQBRdc0Dyturq6+eeqqqpOKelyxx13aNeuXbriiit8vq32OmtUb931wXq9tXynrj9poN3hAAD8SGeXjWmJY4Mja+rV/pOnFuqVxfn62ZQs7wQIAAAAeAmJdqAdXliYp+p6py49tm0DpS1YsEDffPONRo0apfLycr300kv66KOP9M033zTPM27cuIOWCw8PV3p6uqZNm3bQe8XFxbr99tv10UcfNU877rjj9Lvf/U7PPPOMLMvS559/rrvvvrtNsR7Nxo0blZycrPr6euXm5urll1/Whx9+qDlz5uj444/36ra8qUdsuI7tn6LXlu7Qb04coCBH5/RYBAD4v/dWdW7ZGIljg7aY0i9JE7IT9Y/PN+vcsX1aXboPAAAA6AwcnQJtVFXXqKe/ydXxA1I0uI0n4iEhIXrllVc0Z84cORwOHXvssZo3b56GDx/e7njmzJmjs846S2PGjGmeNnr0aP3tb3/TzTffLEm69957NXLkyHZv41B++9vfSnKf6Pfq1UuTJ0/W119/rWOPPdar2/GF2ePT9csXlmnupn2aNjDV7nAAAH6gsLJO87cW6fLj+nZa2RiJY4O2MMboxlMHadaj3+rJuVv1mxMHeGW9AAAAgDcYL98y6vv7TwGbPf7VFt39wQa9fuUUjc1MsDsctEN9o0uT/vKZJmYn6rELx9odDuAN3sgK0oajW3vmm1zd8e46fXztcRrQI8bucHAEv3xhqb7cuE9f3jBNqTHhdocDdBS3VwIA0EUwGCrQBlV1jfrn11t13IAUkuwBLDTYoVmj0/TJur0qrKyzOxwAgB94c/lODe0dS5I9ANxw8iDVN7r04Keb7A4FAAAAaEaiHWiD/8zfruKqev3mxP52h4IOumB8uhpdlt5cttPuUAAANttcUKHVO8t0zug0u0NBK2QnR+knEzP08qI8rdtVbnc4AAAAgCQS7UCrldc26J9fb9HxA1I0JoPe7IGuf48Yjc1M0EuL8uRyUTEDALqzN5fvlMNIZ43sbXcoaKVrZw5QXESIbvvfGnm5FCYAAADQLiTagVZ69IstKq1p0A0nD7Q7FHjJhZMytLWwSt9sLrQ7FACATVwuS28t36Wp/VOUGku970ARHxmq358ySIu3lejN5dydBgAAAPuRaAdaYWdpjZ6Zl6tzRqVpWFqc3eHAS04b3kvJ0aH6z/xtdocCALDJgtwi7Syt0SzKxgSc88ela2R6vO56f4PKahrsDgcAAADdHIl2oBXu+2ijJOl6erN3KWHBQfrRhAx9tqFA+cXVdocDALDBK4vzFRMerJOH9rQ7FLSRw2H057OHqbiqTne9t97ucAAAANDNkWgHjmJFfqneXLFTlxyTrbT4CLvDgZf9eGKGHMbo+QXb7Q4FANDJSqvr9cGaPTpndJoiQoPsDgftMCwtTpce11evLMnXPErBAQAAwEYk2oEjcLos3fLWaqVEh+mq6f3sDgc+0CsuQicP7aGXF+erur7R7nAAAJ3ozeU7Vd/o0gXj0+0OBR1w7YkDlJ0cpRvfWEVbDgAAANuQaAeO4MWF27VmZ7luOWOIYsJD7A4HPvLzqdkqq2nQK4vz7Q4FANBJLMvSy4vyNaJPnIb2ZvyVQBYeEqS7Zw3XjpIa/ZkSMgAAALAJiXbgMPZV1OmejzZqSr8knTmil93hwIfGZiZqfFaCnpqbqwany+5wAACdYEV+qTburdDs8Rl2hwIvmNg3SZce21cvLMzTp+v22h0OAAAAuiES7cBhzPnfWtU2uHTHD4bJGGN3OPCxy4/rp52lNXp/9W67QwEAdILnFmxXVGiQzhzJxfSu4vqTBmhwr1j9/vVV2ldRZ3c4AAAA6GZItAOH8MHq3Xpv9W79+sT+ykmNtjscdIIZg1KVkxqtx7/aKsuy7A4HAOBDhZV1enflbv1wbB9Kw3UhYcFBemj2KFXWNeraV1bI6aI9BwAAQOch0Q4coKSqXn98e42GpcXqsuP62h0OOonDYXTZcX21fne5vthYYHc4AAAfemlhnuqdLv10cpbdocDLBvSI0R0/GKpvNhfqoU+/szscAAAAdCMk2oEWLMvSLW+vUWl1g/72w5EKCeKfSHdyzug09UmI0IOfbqJXOwB0UQ1Ol55fuF3H9k/mrrUu6oLxGTpvbB/9/fPN+mIDF88BAADQOcgiAi28tnSH3lu1W9edNEBDesfaHQ46WUiQQ9fMyNGqHWX6nBNzAOiSPlyzR3vL6/R/x2TZHQp86E9nD9OQXrH61UvLtbmgwu5wAAAA0A2QaAc8thVW6bb/rdWkvom6/Lh+docDm8wa00cZiZH0ageALsiyLD01d6uykiI1bUCq3eHAh8JDgvTkz8YpLCRIl/x7iYqr6u0OCQAAAF0ciXZAUm2DU9e8tFwhQQ49cMEoBTmM3SHBJiFBDl09I0erd5bp43V77Q4HAOBF87cUaeWOMl12XD85aOu7vLT4CP3zp2O1p7xWlz+3RLUNTrtDAgAAQBdGoh2QdMe767R6Z5nuPW+kesVF2B0ObDZrdJr6pkTpbx9uUKPTZXc4AAAveeyrLUqODtOsMWl2h4JOMiYjQfefP1JLtpfoVy8tp10HAACAz5BoR7f3xrIdenFhnq44vp9mDulhdzjwA8FBDv3+lEHasq9Kry7ZYXc4AAAvWLOzTHM3FernU7MVHhJkdzjoRGeM6K3bzhiij9ft1c1vrqE0HAAAAHyCRDu6tVU7SnXTG6s1MTtRvz1pgN3hwI+cNKSHxmcl6IFPv1NVXaPd4QAAOuixL7coJixYP5mUYXcosMHFx2Trmhk5emVJvm55a41cLpLtAAAA8C4S7ei2Csprddl/lio5OkyP/GSMgoP454DvGWN002mDta+iTk98vdXucAAAHbBhT7neW71bP52SqdjwELvDgU2umzlAVxzfTy8szNMf3lxNsh0AAABeRWYR3VJNvVOXPrdU5bUNevKn45QcHWZ3SPBDYzISdObI3nriqy3KL662OxwAQDs98Ml3igkL1qXH9rU7FNjIGKPfnzJQV0/P0cuL8/X711fJSbIdAAAAXkKiHd1Oo9Ola15arlU7SvXABaM0pHes3SHBj/3htEEKchjd8e46u0MBALTDmp1l+mjtXl0yNVvxkaF2hwObGWN0/UkD9OsT+uu/S3fohtdWkmwHAACAV5BoR7diWZb++PYafbp+r24/a6hOHtrT7pDg53rFRehXJ/TXJ+v26ouNBXaHAwBoo/s/+U5xESH6+bHZdocCP2GM0bUzB+i6mQP0xrKduvrFZaptcNodFgAAAAIciXZ0Kw99tkkvLcrXVdP76aeTs+wOBwHikmOy1TclSre9vVY19ZyIA0CgWLC1SJ9vKNBlx/WlNjsO8qsT+uuW0wfrgzV79NNnFqmspsHukAAAABDASLSj23hxYZ4e/HSTzh3bR789aaDd4SCAhAY79JdzhiuvuFr3f7LR7nAAAK3gcln683vr1SsuXJccQ292HNovju2rh2aP0vK8Ep3/+HztKau1OyQAAAAEKBLt6BY+XLNbt7y1WtMHpugvs4bLGGN3SAgwE/sm6ccTM/T0N7lamV9qdzgAgKN4e+VOrd5Zpt+dMlARoUF2hwM/9oNRafr3/03QztIazXp0njbtrbA7JAAAAAQgEu3o8j5cs0dXv7hco9Lj9chPxigkiF97tM+Npw5SSkyYfvfaKtU1UkIGAPxVTb1T93y4USP6xOkHI9PsDgcB4JicZL1y+SQ1uCz98LFvtXBrkd0hAQAAIMCQcUSX5k6yL9PwPnF69pIJigwNtjskBLDY8BDdPWuENu6t0H0ff2d3OACAw3j4i03aVVarW04fIoeDu9jQOkN7x+mNK6coNTZcFz29SG+v2Gl3SAAAAAggJNrRZX209vsk+38umaAYBkGDF0wflKqfTMzQk3O36tsthXaHAwA4wOaCCv3z662aNSZNE7IT7Q4HASY9MVKvXzFFozPi9euXV+ixL7fIsiy7wwIAAEAAINGOLumjtXt01Qvf92QnyQ5vuvn0wcpKitL1r65UaXW93eEAADwsy9LNb65RZGiw/nDaYLvDQYCKiwzRf34+QWeO7K2/frhBt7y1Ro1Ol91hAQAAwM+RaEeX898l+frlC8s0LM2dZI8lyQ4viwwN1oMXjFJhZZ2uf3WlXC56ugGAP/jvkh1amFusG08dpOToMLvDQQALCw7SQxeM0pXT+umFhXm67LmlqqprtDssAAAA+DES7egyLMvSY19u0Q2vrdKUfkl6/hcTSbLDZ0amx+vm0wbrsw0FenLuVrvDAYBub2dpjf707jpNzE7UBePS7Q4HXYDDYfT7UwbpzrOH6cuNBZr9zwUqqKi1OywAAAD4KRLt6BJcLkt/ene9/vrhBp05sree/tl4RYcx8Cl862dTsnTa8J7620cbNX9Lkd3hAEC3ZVmWfv/aKjktS/ecO5IBUOFVF07K1JM/HafNBZWa9ei32lxQYXdIAAAA8EMk2hHw6hqduvbVFXpmXq4unpKlhy4YpdBgfrXhe8YY/fWHI5SVFKkrX1iqbYVVdocEAN3Scwu265vNhbr59MHKSIq0Oxx0QScM7qFXLp+k2gaXZj36rRblFtsdEgAAAPwM2UgEtH0Vdfrxkwv19opduuHkgbrtzCH0YkOnigkP0TMXj5eRdMmzi1VW3WB3SADQrazbVa4731uvaQNT9OMJGXaHgy5sRJ94vfnLKUqJCdNFTy/UFxsK7A4JAAAAfoREOwLWmp1lOuvhb7R2V5n+8aPRump6jowhyY7Ol5kUpScuGqf84mr98sWlanC67A4JALqFqrpGXf3SMsVHhOi+80ZyHACfS0+M1KuXT9aAHjG69D9L9M7KXXaHBAAAAD9Boh0B6Z2Vu3Tu49/KSHrtiik6c2Rvu0NCNzchO1F3nTNc8zYX6da318qyLLtDAoAuzbIs3fzmauUWVunB2aOUFB1md0joJpKiw/TipRM1JjNBv3p5uV5cmGd3SAAAAPADJNoRUBqcLv3l/fW65qXlGtY7Tm9fPVXD0uLsDguQJJ03Ll1XTuunlxbl6am5uXaHAwBd2tPf5OqtFbt07YkDNKVfst3hoJuJCQ/Rfy6ZoGkDUvSHN1fria+22B0SAAAAbGa83OuSLpzwmbyial3z8nKtzC/VTyZm6LYzhzLoKfyOy2Xp6peW6f3Ve3TXOcP144nUC0an8Ea9DNpwBIxvNhXqp88s1MwhPfTYT8YyPgtsU9/o0vX/Xal3Vu7SL6f10w0nD6SEEdqKXxgAALqIYLsDAFrjfyt36eY3VssY6dGfjNFpw3vZHRJwSA6H0QMXjFJ1/VLd/NZqhQU79MOxfewOCwC6jM0FFbrqxWXqnxqj+84fRZIdtgoNdujBC0YpJjxYj365ReW1DbrjrGH8XgIAAHRD9GiHXyuvbdCf3lmn/y7dobGZCXpo9ij1SYi0OyzgqGobnPr5s4s1f0uRHpo9mnEE4Gv0aEe3sLe8VrMe/Vb1TpfeuHKK0hM5JoB/sCxLf/1wox7/aotmjU7T384doeAg7rxEq3BVBgCALoJEO/zWZ+v36uY316igola/nJaj35zYnxMWBJTq+kZd/MxiLc0r0WM/GaOThva0OyR0XSTa0eWV1TTogifmK7+4Wq9cPpkxWuCXHvlis+75aKNOGdpTD/1olMKCg+wOCf6PRDsAAF0EiXb4neKqet3xzlq9tWKXBvaI0d/OHaGR6fF2hwW0S0Vtgy56epHW7irTAxeM0hkj6NkOnyDRji6torZBFz69SOt3levpi8fp2P4pdocEHNa/5uXq9nfW6fgBKXr8wrGKCCXZjiMi0Q4AQBdBoh1+w+Wy9Obynbrr/fUqq2nQVdNzdNX0HAY8RcArq2nQL55drCXbS3THWUN10eQsu0NC10OiHV1WVV2jLv7XIi3PK9Wj3B2EAPHq4nz9/o1VGp+VqKd/Nk4x4SF2hwT/RaIdAIAuggwmvCIrK0vGmP0ePXse/UT4tttu0/DhwxUdE6uwyCj9+IzpMrnz9c41U3XtzAEk2RFQXnvtNU2ZMkVJSUkKDw/XwIEDdeeddyoiyNJzP5+oEwal6o9vr9UDn3ynlhc5lyxZopNOOkmJiYlKTEzUiSeeqIULF9q4JwDQOerr63X++eerb9++ioiIUEpKik499VQtXbpUklRW3aALn16opdtL9NDs0fsl2evr63XHHXcoJydHERERysnJ0W233aa6ujq7dgfdzM6dOxUdHS1jjCorK/d77/zx6fr77NFatr1EFz61UPOXrNBJJ52kyMhIJScn68orrzxoGQAAAAS2YLsDQNfx4x//WNdcc03z69DQ0KMus7ewRMljTlLB4Fj1jgxTRtkqffav27T2tCEafO65vgwX8LqioiLNmDFDN9xwg+Lj47Vo0SLNmTNHe/bs0cMPP6zHLxyrG99YrYc+26SiqjrdftYw7dq5QyeeeKLGjBmj5557TpJ0zz33aObMmVq9erUyMzNt3isA8B2n0yljjG666Sb169dP5eXleuCBBzRjxgx9OneB/vj5Pm3dV6VHfzJWpwzb/wL+jTfeqMcff1x33nmnRo8erWXLlumWW25RaWmpHnroIZv2CN3JDTfcoOjoaFVVVR3y/TNH9lZESJAuf2aupt10mUYPH6xXXnlFRUVF+t3vfqfdu3frrbfe6tygAQAA4DOUjoFXZGVl6dxzz9W9997bqvnLaxv01Ndb9fQ3uaprdOmSqdm6ZkaOYsJDdMwxxygpKUn/+9//fBw14Hs333yzHnnkEZWUlMgYI8uydPeHG/TEV1t1wqBUDatYpN/+5lcqLi5WXJx7YL+SkhIlJyfr4Ycf1pVXXmnzHiBAUDoGXUZlZaUSk5KUNvMShY/+gf7507GHrMnes2dP/eQnP9F9993XPO26667TCy+8oL1793ZmyOiGvv76a5199tn6wx/+oBtuuEEVFRWKjo4+5LxX/PYWPfmP+zX5llf1yjUnKC0+Qu+8847OOussLV68WOPGjevk6OFnKB0DAEAXQY92dKraBqeem79dj365WSXVDTpteE9df9JA9Uv5/sQkKSlJ9fX1NkYJeM+Bv8/GGN106mD1iY/Q7e+s09x1GxUUHKyoqKjmeaKjoxUcHCwvXwgFgICwbFe1nCZYDfUNevvySRrRJ/6Q8zU0NDRfoGwSHx/P3074nNPp1DXXXKNbb71V8fHxR52/JH+Txowdq7LGEJ3/+Hy98IuJmjlzpowxeu+990i0AwAAdBEUwIbXPP300woNDVVcXJzOPfdcbd++vfm9RqdLLy3K07R7vtSf31+vYWlxeufqqXr0J2PVLyVajY2NKi0t1QsvvKCPP/5YV1xxhY17AnSM0+lUdXW1vvnmG/3973/XlVdeKWP276x00eQsvXjpJIUPmCKnI1TnXXyFCgoKVFBQoGuvvVYJCQk677zzbNoDAOhclmWpoaFBd7+xQGdddKUcjiC9du9vD5tkl6Rf/OIXeuKJJzRv3jxVVlZq7ty5euyxx3T11Vd3XuDolh5//HHV1dXpqquuatX8tbW1SoqN0kuXTVJ1faPOfXy+NuytksPh0Pr1630cLQAAADoLPdrhFT/4wQ80adIk9enTR+vXr9ftt9+uY489VstXrNTX26v0j882a2thlUalx+v+C0ZqSr/k5mUXLFigyZMnS5KCg4P18MMP6+yzz7ZpT4COi4qKah6M76c//anuueeeQ843ITtRH/7hB/qxo0bvPHKDDOTSQgAAImtJREFU3nrhaUlSr1699NFHHykl5eBSCQDQFc35012647ZbJEkRsQn6+MP3NWnEoCMuc/fdd6umpkZTp05tnvbLX/5St956q09jRfdWVFSkP/7xj3r++ecVEhLSqmVycnL04osvamBqpP57xWT97JnFOueO5+R0OlVcXOzjiAEAANBZqNGONrEsS06ns/m1MUZBQUEHzbd8xSqNGzdGWaddLueQ0zSwR4yuP2mAZg7pcVDP3qqqKq1fv16lpaV677339PDDD+s///nP/7d35+FVVff+x98rJ3NICElISAiESWWWQVQUFaq21GqrVVv06lUp3lq13l/tPHgN1Gpta6+21dZqnWoprda2tqJ1KIhFLoMoVhkEQghDgECAjCc5w/r9sXdCEjInZ0jyeT3Pes45e8pae53stc93r70211xzTcjLIxIKGzdupKamhnXr1rFkyRKuvfZaHnnkkVaXLS0t5bzzz4f0fCpHz2Ps0BSSd7zB1g/f5+2332bkyJFhzr30URqjXaJeW+cQa3Ye4fbf/JODpfu54rRkdrz5AuvXr2fVqlVMnDixze396Ec/4oc//CFLlixh6tSpbNq0ibvuuos77riDJUuWhKNIMgDdcsstlJSUsHz5cgCeeuopbrrppnbHaN+6dSuTJ09m0aJFFBYW8tHu/Vx21TVU7NvB1LPOY9OalWEsgUQhjdEuIiLSTyjQLl2ycuVK5s2b1/j5ggsuYOXKlY2fvb4Az72zl1+t3Mn6n9xE9pgJ/ObJp7h4Qg4xMZ07h1y4cCGvv/46JSUlvZ19kbB75plnuOGGG9ixYwdjx449af6dd97JCy+8wPbt23l5cxnf/fO/CfjqKXviSyy46gp+/vOfRyDX0gcp0C5Rr+U5xLnnnc8FX/kFS9eVMDozhYcWTGdK/mD8fj+TJk3irLPO4plnnml1W4cPHyYvL4+HH36Ym2++uXH6o48+yu23386+ffvIzs4OeZlkYPnwww+ZPn06q1atYvx4546LpUuXctttt7F3714yMjJISkpqdd0nnniCr3zlK1RUVBATE8NNX1jEX15dhTd1OIU/eZivfvzUkzqjyIChihcREeknNHSMdMnMmTNZv3594+fU1FQAquv8LFu/h1+v2snBijpmjExneEYS50/I4ROThnXpb8yYMYMnn3wSv99PbKy+otK3zZgxA4Bdu3a1GmjfunUrkyZNIi4ujk+fnsfMgiF89Y/v8dfkYbz41rv8T2UdQ1MTwp1tEZFe13AOYa3lXzsO88TaA/x+XQk3nTOar378VFISnDY/NjaWKVOmUFRU1Oa2ioqK8Pl8TJs2rdn06dOn4/f72b17twLt0uu2b9+Oz+drHPKwqfz8fL7whS/w+OOPt7ruwoULufbaa9m+fTvZ2dlkZWXxfGYm5378Sn6xYgc7DlXx46unkprYueFoRERERCT6KIopXZKamsoZZ5zR+PlwVR0PvLqNZ9bs5nitj7NGZ/DTz00jrbaU6XfsYObtt3b5b6xevZr8/HwF2aVfWL16NQCjR49udX5BQQHLly+nvr6e+Ph4hqcn8cT108m/az/H02dw4QMr+cb88Vx75shO3xUiIhKNUlNTGTp6AoUvfsiKbUEmjRnHDz87lSn5g5st5/V62bhxI+eee26b2yooKACcobpmzZrVOP2dd94BYNSoUb1fABnw5syZw4oVK5pNe+WVV7j//vtZvnw5Y8aMaXf9xMREpkyZAsDTTz9NMBhk6X1f4c+bj3Pfy1v5zMOrefS6mZySkxqyMoiIiIhI6CiSKd2y+0g1j71VxHMb9nJs21pS965h0YIrOffUZN5/7TnuueceRo4cyY033ti4zjPPPMPChQvZuXMnBQUF7N69m4ULF7JgwQLGjh1LVVUVf/7zn1m2bBm//OUvI1c4kW6aP38+F110EZMmTcLj8bB69WoeeOABPv/5zzf2Zh83bhwXXHABv/mN8+DTRYsW8fjjj3PFFVdw6623Yq3l4YcfprK8jBeWfZffbYfv/eUDnn9nLz+4YjKT8ga3lwURkah0qNLLL/65g6VrS4jzxPC9T03gxnNG8dwf/8CPX36Z+fPnk5eXR2lpKY888gilpaXceeedjeu3PIfIycnh8ssv55vf/CZer5epU6fy3nvvUVhYyNVXX62HSUtIZGVlMXfu3GbTiouLATjvvPMax2hv2dZXVFTwgx/8gPPPP5/Y2FhWrFjBAw88wGOPPUZmZiaLzstkyvDB3Lb0XT7z8Gp+dNVULp2aF86iiYiIiEgvUKBduuT9vcd49M0iXv6glNiYGK6cOZw5F83np99/i4fu+S6Ljx0jMzOT+fPnc++995KWlta4bjAYJBAI0PBcgPT0dPLy8rj33nspLS0lPT2diRMn8tJLL3HJJZdEqogi3TZr1iyeeuopiouLiY2NZcyYMdx3333ccsstjcv4/f5mDwOcOXMmr7zyCosXL+b6668HYMqUKbz22mvMnTubS+da/vLePu75+xYu+/m/uO7sAr78sVM0nIyI9AkVXh+PrSri8bd2UR8IsmDWCO648BRy0hIBGD9+PM8++yx33nknR48eJTc3l7POOosNGzYwadKkxu20PIcAp0fwkiVL+NnPfsb+/fsZPnw4X/ziF7nrrrvCXk6Rplq29R6Ph3fffZfHHnuM2tpaJk+ezHPPPcfll1/euMxZYzJ56Y453Pq7jdy+9F02FB/lm/PHkxTviUAJRERERKQ79DBU6VAwaHlzexmPrSri7Z1HSE2M5bqzC7jpnFFkuz+URSS0jtf4+Mmr21i6roSE2BgWzRnNovPHkKaxXMWhh6FKVDlU6eXpt4v57ZrdVHj9XDo1l69+/DRGZ6VEOmsiUa3eH+SHL2/lidW7GJOVwo+vPp2ZBUMinS0JLY0NKCIi0k8o0C5tqq7z88LGvTz5djFFZdXkpCXwhTmjuebMkXpQk0iE7DpczQOvbuPv75cyJDmOL80dy3+cVdD4EEEZsBRol6hQVFbFY2/t4k8b9+ILBJk/aRi3zRvH5OEa9kqkK97ecZivP/8+pcdrufn8MXzlolNJjFPv9n5KgXYREZF+QoF2Ocme8hqeWVPMsvV7qPT6OT1/MAvnjOaTk3OJj42JdPZEBPhg33Huf2Urb20/zOCkOK4/u4AbzhmlIWUGLgXaJWICQcuKrYd4du1u3vyojDhPDFfNzOfm88aoB7tID1R6ffzgpS0sW7+HcdmDKLxsEnNOyYp0tqT3KdAuIiLSTyjQLoAzPMyaoiP8ds1uXt18AGMMn5w8jJvOHc2MkekYo/M/kWi0seQov36ziH9sPtAY3Lph9ihOG5Ya6axJeCnQLmFXVlnHHzfsYenaEvYdqyU7NYEFZ47k+rMLdNFPpBet2HaIu/7yAXuP1nLh+Gy+86kJjB06KNLZkt6jH1oiIiL9hALtA9zhqjqef2cvy9aVUHykhvTkOK5xfyTnpSdFOnsi0klNh2uo9weZWTCEBbNGcOnUPD1IbWBQoF3Cos4f4I0th/jTO3tZ+VEZgaDlnLGZXH92ARdNzCHOozvfRELB6wvw5OpiHl6xA68v4D4cfRyZg3RRqx9QoF1ERKSfUKB9AKrzB1ixtYy/vreP17ccxBewnDk6g2vPHMn8ycM0/qNIH3akqo4XNu7j9+tKKDpcTWpiLJ8+PY9Pn57HrFEZxMTot1w/pUC7hIy1lvf3Huf5d/by4qb9HK/1kZOWwGdn5HPVzHz1rBUJo7LKOn762kf8YX0J8bExLJg1kkXnjSZ/SHKksybdp5MzERGRfkKB9gHCHwiyvvgoL27ax0vvl1Lh9ZM1KJ5Pnz6ca88awbhsDTMh0p9Ya1m3q5zfryvhlQ8P4PUFyR2cyGWn53HZ1DwmD0/TkFD9iwLt0uuKyqp46f1SXty0n+2HqkiIjeETk4Zx1cx8zh2XhUcX7kQiZsehSn71ZhF/eXcfFvj06XncfN4YJualRTpr0nU6mIqIiPQTCrT3Y9V1ft7aXsarmw+yYushjtb4SI738IlJw/jMtDzmjMsiVrd4i/R71XV+Xt9ykBff28+q7WX4Apa8wYlcOCGHCydkM3tsJgmxupOlj1OgXXrFnvIa/vb+fv6+qZTNpRUAzBo1hCum5/OpqbkMToqLcA5FpKn9x2r5zb928ft1JdTUB5gyfDBXn5HPp0/PIz05PtLZk85RoF1ERKSfUKC9H/H6AmwsOcraonLW7jrCxpJj1PuDDE6K42Pjs7loQg7zxg8lOT420lkVkQg5VlPPq5sP8saWg6z66DC1vgDJ8R5mj8nknHFZzBmXxak5g9Tbve9RoF26xVrLzrJq3thykOX/LmXT3uMATBuRzqVTc/nU1FxyB+uZLSLR7lhNPS9s3Mdz7+xlS2kF8Z4YLp6YwycmD+OCU4fqIll000mXiIhIP6FAex/l9QXYdqCSzaUVfLj/OJv3V/DBvgrqA0GMgYm5acwek8mFE3I4Y9QQPZxMRE7i9QVYU3SEN7Yc5F/bD1N8pAaArEHxnD0mkxkjhzB9ZDqT8gYTH6tjSJRToF06zRcIsn5XOa9vOcQbWw+y2/3fnzw8jUun5vGpKbmMyNB4zyJ91Yf7j/Pchr38bdN+jlTXExtjmDUqgwsnZHPBqUMZO3SQntkSXVQZIiIi/YQC7VHIWsvRGh/7j9Wy71gt+xuTt/FzWVUdDVU3KCGWiblpnD5iMGePyeSMURnqtSIiXbbvWC2rdxzm7R2HWbernP3HvQDEx8YwOS+NSXmDGZ+byoTcNE7LSSUlQXfHRBEF2qVN1lpKymtYs/MIb+04zKptZVTW+YmPjeGcsc5F+Y+Nz2Z4unqui/QngaDlvT1HnYtqWw7y0cEqAIYkxzGzIINZo4Yws2AI43PTGKQ2PZIUaBcREeknFGiPAK8vwIHj3iaBdOf9/uMnAuteX7DZOgmxMQxPTyIvPYm89ETy0pMYPyyVibmDyR+SFPW9UgoLC1m8eHGksyESFe6++24KCwsjnY0OHTju5d2So2wsOcp7e46xpbSSqjp/4/zh6UmMzkphVFYyozJTKMhMYVhaItlpCWSmxOsZEOGlQLs0CgQtOw5V8d6eo6zbdZQ1Ow83XjgbmprAx07L5sIJ2cw5JatPDCencwjpq6Ktvd9TXsOaoiNsKC5nQ/FRig5XN84bmZHMhNxUxg9LY8zQFEZmJFOQmcKQ5DgNJxd62sEiIiL9RPT/uuqDGnqk7z5STUl5DcWHa9hdXk3JkRp2l9dQVll30jrZqQnkusHzj52W7QbUk9zgeiIZKfE6yRWRsBo2OJFPTsnlk1NyAefYtvdoLVsPVLKltIKdZVUUH6nhb5tKOV7ra7ZujIGsQQnkpCWSk5ZARko8aYlxpCXFkZYY677GkZoYS0pCLIMSTrwmxsXoeCfSSfX+IDvLqth2oJItByrYtOcY/957nOr6AAAZKfGcPSaDL43JZPbYTMYO1TMYRAaqERnJjMhI5nNnjACgrLKOTXuOsfVABVtKnWPIq5sP0rQfVmpCLCMzkynITGbEkGS3XU9k2OAEslOdi+t6oLqIiIiIQ4H2bgoGLQcqvBQfcQLoxUdqKCmvZveRGkqO1FDZpNcnwLC0REZmJjP31KGMyEhu7J0+PD2JnME6QRWR6GeMafyRfvHEnGbzjlbXU1Jew8EKL4cq6zhU4eVgRR0HK73sPVrLB/sqqPD6qHGDf+3xxBiS4z2NwXcnAO8hJT72pGnJzaZ5mgXsG6bp+Cp9Xb0/yMEKL3uO1rD7SEOqZmdZFUVl1fiDTlQszmOYkJvGlTPzmTYinWkj0hmdlaLAuoi0amhqAhdNzOGiJm261xegpPzEcWZPudNRaGtpJa9vPkR9IHjSdoYkx5GTlkh2WiJDByWQOSiejJR4MlPi3fcJje/7wl00IiIiIt2loWPaYK2lwuvnYIUzLnpJkx+2u8trKCmvod5/4kQzzmPIH5Ls3mbpvDpDKThBqcQ4BXpERHyBIJVePxW1Piq8Pipq/VTV+amu81Nd3+R9XaDx/UnT6p3PvkDnmpw4j3GC7m5QPtXtUT/YTU3fn5gW2/g+Kc7TFwKVGjqmD7HWUlnn53iNj2M1Po7V1ruvPsqr6jlQ4eVghZcDx53XI9X1zdaP98SQn5HE6MwUThuWymnDnOEeRmel6MHFIhIy1lqO1fg4WOleTK/wnriw7h63DlfVc7iqjjr/yQF5gMS4GDJTTgTjM1LiyUiOJ9W9y81Jzt1vDdPSkuJIjveQENtv73jrl4USEREZiPp1oD0YtNQHgtT5gnj9Aep8QWp8fipqmwZ5fFR4/Ryv9XGo8sRJ4sEK70njpCfFeShwb50scIPoBRnOa+7gRI1HLCISRnX+ANV1gcYgvROUD7QIzp+Y1jC90j3mH3fbgUqvv92/E+cxpCY6AfekeI/z2vR9vJPiPTF4YgyxMYYY99UTY/AYg8fjfD5zdCbTRqSHYnco0N5LrLXU+YPU+YPU+4PueUSg8XzixGuAene5mnrnO1ZTH3CTv/G1ui5AbX2AanfasZp6Krx+AsG2d3dmSrw7NIM7RIM7TEP+kGT3nCMJT5Q/m0VEBi5rLTX1AcqrnaB7eXU9R6rrOVJVT3l1XZP3J1Ktr+M73sB5QHtCbAwJsR4S4068T4iLcdpf4yRPjMEY5y65E9Nw3seYVhvNlkH8lsucMzaTBWeO7N5OaZ8O6CIiIv1EVN+7948PD/DAq9sIBC3WQtBagu6rtc7DvhqmWXvifTDo/Ehu7dbGtqTEexiamkB2WiKn56eTk5bQZAzCRAoykxk6KKG/9qIQEelzEmKdYWEyUuJ7tJ1A0FLp9TUG35umilonKF/p9VHrC+D1OUHTWp8TMC31Oe9r652ga9CCPxgkELRuG9X8b33rk+NDFWiPOv/ee5yvPbcJ68bvG67rN+yShgv9jbuog/kn1m++vZbvu7Juw/zG84Yunju0Jj42huR4Z6ijpHgPKe6FmJy0RJLjPaQnx5GeFE96snPHRHpyvDstjsHuPPVKF5G+zBjTOMzbiIzkTq3jCwSp8joXwxsugle6rxVuG9y085RzQTTgvPqcV3/A+T3oDwapDzT9rWgJBJ22IRC0BFrraNayHWkljyM7WRYREREZuKI60J6aGMvYoYMaex7EGKcXgnFfY9xeCsacmNcw3wnAxJAY57wmxDm9HZLiPM2GBmh4GJ96o4uIDEyeGOMGO3sWsG9N0P1B3xB4j/UMnIu1iXExjM5KAaDhGnXjK41vmr40Xsw+8bn9+c23YdpYp435jRtxziEaekTGe2KavHpI8MQ09qCMd3tONv8cQ3J8LMkJHpLjPDqfEBHphjhPDENS4hnSw4vnIiIiIpHUr4eOERERGSA0dIyIiEjfNHCuwouIiPRz6nYlIiIiIiIiIiIiItIDCrSLiIiIiIiIiIiIiPSAAu0iIiIiIiIiIiIiIj2gQLuIiIiIiIiIiIiISA8o0C4iIiIiIiIiIiIi0gMKtIuIiIiIiIiIiIiI9IAC7SIiIiIiIiIiIiIiPaBAu4iIiIiIiIiIiIhIDyjQLiIiIiIiIiIiIiLSAwq0i4iIiIiIiIiIiIj0gLHW9trGFi9e/AqQ1Wsb7J48YH+E8xAKKlffonL1LSpX36Jynezw3XffPb8nfzxK2vCO9Ne678tUJ9FHdRJ9VCfRJ5rqpMdtuIiIiEQJa22/SoWFhTbSeVC5VC6Vq28llatvJZVr4Cbto+hLqpPoS6qT6Euqk+hLqhMlJSUlJSWlUCQNHSMiIiIiIiIiIiIi0gP9MdC+ONIZCBGVq29RufoWlatvUbkGLu2j6KM6iT6qk+ijOok+qhMRERHpdb06RruIiIiIiIiIiIiIyEDTH3u0i4iIiIiIiIiIiIiEjQLtIiIiIiIiIiIiIiI9oEC7iIiIiIiIiIiIiEgP9KlAuzHmv4wxK4wxx4wx1hgzqpVlhhhjfmuMOe6m3xpj0jvYrjHGFBpj9htjao0xK40xk0JVjg7yMsotW2vp6+2sN7eNdcaHM//tcfdry/wt68R6VxpjNhtj6tzXK8KR384wxmQYY35ujNnqfnf2GGN+aYzJ7GC9G9uor8Rw5b2NfN1qjNlljPEaY94xxpzXwfIXuMt5jTFFxphbwpXXzjDGfNsYs94YU2GMKTPG/M0YM7mDddr6H5wfrnx3xD1etczfgQ7WmWKMedP9nu4zxvyPMcaEK8+dYYwpbmPfv9TOOq0tH9HvoTHmfGPMi+5+tsaYG1vM71abE83HwlAzIWr/pfd0t42X3tPVNlxCqztttfSuULXHIiIiIm3pU4F2IBl4FShsZ5mlwAxgvptmAL/tYLvfAL4KfBmYBRwCXjPGpPYwv92xB8htkW4FLPB8J9af1GLd7aHJZrc9SfP8fbG9hY0xs4E/AL8DprmvzxljzgptNjstDxiO8x2aAlwHnA/8vhPr1tCirq213hDls0PGmM8DDwH3AtOBt4GXjTEj21h+NLDcXW46cB/wc2PMleHJcafMBR4BzgE+BviB140xGZ1Ydz7N6+efIcpjd22jef6mtLWgMSYNeA04iHOM+2/g68Cdoc9ml8yieZlm4Bz7/tjBeje3WO/pEOaxMwYBH+Ds59pW5ne5zekDx8JQC1X7L72rS2289J6utuESNp1uqyUker09FhEREWmPsdZGOg9dZow5A1gPjLbWFjeZPgHYDMyx1q52p80B3gLGW2u3tbItA+wHfmGt/YE7LQnnROtr1tpHQ1ycDhljXgOstfbj7SwzF1gBDLXWHg5T1rrEGLMS+MBae3sX1vkDkGGtvbjJtNeBMmvtNb2fy54zxlwC/B1It9ZWtLHMjTjfuUHhzFt7jDFrgfettTc3mbYdeN5a++1Wlr8f+Ky19pQm0x4HJllrZ4cjz11ljBkEHAcut9b+rY1lRgG7gFnW2g1hzF6nGWMKgauste32zm+y/JeA+4Eca22tO+17wJeAfBulDYEx5rs4FwRyG/LdyjIWuNpa25kLkWFnjKkCbrfWPuV+7lab0xePhaHQm+2/9K7utPHSe7rahkvodbWtltDqrfZYREREpD19rUd7R2YDVTi9eBqsBqpxerS2ZjQwDKenHABuQGdVO+uEjTFmDHAh8OtOrrLBGFNqjHnDGDMvhFnrrgXGmMPGmA+NMT/pRI+R2TSpG9c/iIK6aUcaUIfTY709ScaY3caYvcaYvxtjpochb60yxsQDMzl5X79K2/u6rbo5wxgT17s57DWpOMe9o51Y9gVjzCFjzGpjzFUhzld3jHFvdd5ljFnmHivaMht4q0Ww+h84d2SMCmUmu8v9AfwF4Nm2guxNPOQeV9YbY24xxkRz29bdNqcvHgvDqTvtv/S+rrbx0gu62YZLeHSlrZbwiurfgCIiItI3RXMwojuG4fTua+yd6b4/5M5rax1whlRo6mA764TTIqAM+GsHy5Xi9E69Evgszq2qb0TZ+JxLgf8A5gHfx8nrnzpYZxjRWzcncccD/j7wmLXW386i24CFwGeAawAvsNoYc0o764RSFuCha/u6rbqJdbcXjR4C3gPWtLNMFfA14HPAJcAbwB+MMdeFPHedtxa4EWd4jJtx6uJt0/azAdqqq4Z50ehinB/Bj3Ww3P8AnwcuApYBDwDfCW3WeqS7bU6fOhZGQHfaf+ld3WnjpXd0pw2X0OtqWy3hFe2/AUVERKQPio10Bowx9wDf7WCxedbalWHITsh0p5zGmFjgJuBpa62vvRXd2+Kb3hq/xh0C4+s4t86HRFfKZa1t2iv/38aYImCtMWaGtXZjqPLYHd2sr0HA34B9OGM+tslau4YmwV5jzNs4AeAvA3d0K9PSLmPMT4E5OENLBNpazh166YEmkzYYY7Jw6vTZ0Oayc6y1Lzf9bIz5P6AIuAH4aUQy1ftuBtZbaze1t5C19vtNPr5njPHg/O/eE8rMSc8NlPa/L+uvbbxIOAyQtlpEREREmoh4oB14kI6DVyWd3NYBYKgxxjT0anOHH8h257W1DkBOi7+T08463fEgXS/nZTg9Kh7v5t9cCyzo5rqd9SDdr78NQAA4BWjrR/gBnLpoqrfrpjUP0oVyuUH25e7HS7v6UFNrbcAYswFnX0TCYZy66Mq+bqtu/O72ooYx5n9x/hfmWWuLurGJtTgXvaKStbbKGPMhbX9/2qqrhnlRxRiTjXO3x23dWH0tkGaMybHWtuylFg262+ZE6lgYSg8S2fZfOvYgoW3jpXd0pw2XMOtEWy3hFa7fgCIiIjKARDzQ7vYe7a2g3Bqcp8vP5sQ4rbOBFJqP29rULpyTqYtxHrCGMSYROA+nN3iv6GY5bwbetNZ+1M0/Ow1nSJmQ6WH9TcG51bm9PK7BqZsfN5l2MW3XZ6/oSrncMWhfBgww31pb1dW/5waEpgLt9t4NFWttvTHmHZx9+1yTWRfT9q3/a4ArWky7GNjQ0R0Y4WSMeQhnaJF51tqt3dzMNEL8v9QT7jFrPM4DkVuzBrjfGJPY5CLQxTgPASsOfQ677Eac5xz8vhvrTsMZiulY72WnV3W3zYnIsTCUoqD9lw6EoY2XXtDNNlzCrBNttYRXWH4DioiIyMAS8UB7VxhjhuH08D7VnTTRHRO7xFpbbq3dYox5BXjUGPNf7jKPAn93h1bBGDMcZ8zlb1tr/2yttcaYB4HvGGO2Ah8B38MZp3lpuMrWkjFmJPAJ4D/bmP8MgLX2P93P/w8nYPYhEA9cB1yOM0ZqxBljxuKM3boc50f7RJzhOd7FeWBdw3JvAOustd92Jz0ErDLGfAv4C05gdx7OECAR5wbZX8V5AOrlQIoxJsWdXW6trXeXa1YuY8zdwP8B291178AJtH8prAVo7qfAb40x63Dq5Bach2X+Ck7+zrnTb3f/fx4FzsUJkF4T1ly3wxjzMHA9Tt0cdY8hAFUNF0SMMfcBZ1prL3Q/3wD4cL6bQZw7S24Dvhne3LfNGPMTnGGKSnB67N6FE1B82p3frEw4x7K7gafcoSBOBb4FLG46pnU0cC86LQKWtbxoZYy5HbjdWjve/dxw188aoBbn2LAE+LW1ti6sGW+ez0HAOPdjDDDSGDMN55hQ0pk2p68dC0OtN9p/CZ3OtvESUu224RJ+HbXVEnq90R6LiIiIdIm1ts8koBCwraQbmywzBOc25wo3PQukN5k/qpV1jLvtUpyekG8CkyNc1sVAOZDYxvyVwMomn7+BE7Stddd7C7gk0nXWJH8j3P16BKen6g6cwFFGi+WKgadaTLsK2ArUA1uAz0a6PE3yNreN76QF5rZVLuB/gd3uvjgE/AOYHQXludXNax3wDnB+W985d9oFOEMC1OH0DLol0mVokb+26qawyTJPAcVNPt8AbAaq3WPIBuC6SJelRbmW4fRGr8d5JsCfgIltlcmdNgVY5R7jSnEC7ybSZWmlbPPcOjqzlXmFuM+4dD/PxwnkVbr19W/gv4HYCJehrePCU+78DtucvnYsDMM+LWxjn97YZJl223+lkNZPp9p4pZDXQ5ttuFJE6qPdtlopLHXQ4/ZYSUlJSUlJSakryVgbVZ0ZRURERERERERERET6lJhIZ0BEREREREREREREpC9ToF1EREREREREREREpAcUaBcRERERERERERER6QEF2kVEREREREREREREekCBdhERERERERERERGRHlCgXURERERERERERESkBxRoFxERERERERERERHpAQXaRURERERERERERER6QIF2EREREREREREREZEe+P8pF2jVBI/PWwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1490.4x662.4 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(trace, var_names=\"model/layer/l3_w\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction\n",
    "\n",
    "To obtain posterior predictive samples for a test set `x_test` we simply call the `model` generator function again with the test set as argument. This is a nice improvement over PyMC3 which required to setup a shared Theano variable for setting test set values. Target values are ignored during predictive sampling, only the shape of the target array `y` matters, hence we set it to an array of zeros with the same shape as `x_test`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</svg>\n",
       "<style>/* CSS stylesheet for displaying xarray objects in jupyterlab.\n",
       " *\n",
       " */\n",
       "\n",
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       "\n",
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       "  max-width: 700px;\n",
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       "\n",
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       "  /* fallback to plain text repr when CSS is not injected (untrusted notebook) */\n",
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       "\n",
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       "  padding-bottom: 6px;\n",
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       "\n",
       ".xr-header > div,\n",
       ".xr-header > ul {\n",
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       "\n",
       ".xr-obj-type,\n",
       ".xr-array-name {\n",
       "  margin-left: 2px;\n",
       "  margin-right: 10px;\n",
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       "\n",
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       "\n",
       ".xr-sections {\n",
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       "  display: grid;\n",
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       "\n",
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       "\n",
       ".xr-section-item input:enabled + label {\n",
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       "\n",
       ".xr-section-item input:enabled + label:hover {\n",
       "  color: var(--xr-font-color0);\n",
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       "\n",
       ".xr-section-summary {\n",
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       "\n",
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       "  display: inline-block;\n",
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       "\n",
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       "  color: var(--xr-font-color2);\n",
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       "\n",
       ".xr-section-summary-in + label:before {\n",
       "  display: inline-block;\n",
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       "  font-size: 11px;\n",
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       "  text-align: center;\n",
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       "\n",
       ".xr-section-summary-in:disabled + label:before {\n",
       "  color: var(--xr-disabled-color);\n",
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       "\n",
       ".xr-section-summary-in:checked + label:before {\n",
       "  content: '▼';\n",
       "}\n",
       "\n",
       ".xr-section-summary-in:checked + label > span {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-section-summary,\n",
       ".xr-section-inline-details {\n",
       "  padding-top: 4px;\n",
       "  padding-bottom: 4px;\n",
       "}\n",
       "\n",
       ".xr-section-inline-details {\n",
       "  grid-column: 2 / -1;\n",
       "}\n",
       "\n",
       ".xr-section-details {\n",
       "  display: none;\n",
       "  grid-column: 1 / -1;\n",
       "  margin-bottom: 5px;\n",
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       "\n",
       ".xr-section-summary-in:checked ~ .xr-section-details {\n",
       "  display: contents;\n",
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       "\n",
       ".xr-array-wrap {\n",
       "  grid-column: 1 / -1;\n",
       "  display: grid;\n",
       "  grid-template-columns: 20px auto;\n",
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       "\n",
       ".xr-array-wrap > label {\n",
       "  grid-column: 1;\n",
       "  vertical-align: top;\n",
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       "\n",
       ".xr-preview {\n",
       "  color: var(--xr-font-color3);\n",
       "}\n",
       "\n",
       ".xr-array-preview,\n",
       ".xr-array-data {\n",
       "  padding: 0 5px !important;\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-array-data,\n",
       ".xr-array-in:checked ~ .xr-array-preview {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       ".xr-array-in:checked ~ .xr-array-data,\n",
       ".xr-array-preview {\n",
       "  display: inline-block;\n",
       "}\n",
       "\n",
       ".xr-dim-list {\n",
       "  display: inline-block !important;\n",
       "  list-style: none;\n",
       "  padding: 0 !important;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list li {\n",
       "  display: inline-block;\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "}\n",
       "\n",
       ".xr-dim-list:before {\n",
       "  content: '(';\n",
       "}\n",
       "\n",
       ".xr-dim-list:after {\n",
       "  content: ')';\n",
       "}\n",
       "\n",
       ".xr-dim-list li:not(:last-child):after {\n",
       "  content: ',';\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-has-index {\n",
       "  font-weight: bold;\n",
       "}\n",
       "\n",
       ".xr-var-list,\n",
       ".xr-var-item {\n",
       "  display: contents;\n",
       "}\n",
       "\n",
       ".xr-var-item > div,\n",
       ".xr-var-item label,\n",
       ".xr-var-item > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-even);\n",
       "  margin-bottom: 0;\n",
       "}\n",
       "\n",
       ".xr-var-item > .xr-var-name:hover span {\n",
       "  padding-right: 5px;\n",
       "}\n",
       "\n",
       ".xr-var-list > li:nth-child(odd) > div,\n",
       ".xr-var-list > li:nth-child(odd) > label,\n",
       ".xr-var-list > li:nth-child(odd) > .xr-var-name span {\n",
       "  background-color: var(--xr-background-color-row-odd);\n",
       "}\n",
       "\n",
       ".xr-var-name {\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-var-dims {\n",
       "  grid-column: 2;\n",
       "}\n",
       "\n",
       ".xr-var-dtype {\n",
       "  grid-column: 3;\n",
       "  text-align: right;\n",
       "  color: var(--xr-font-color2);\n",
       "}\n",
       "\n",
       ".xr-var-preview {\n",
       "  grid-column: 4;\n",
       "}\n",
       "\n",
       ".xr-var-name,\n",
       ".xr-var-dims,\n",
       ".xr-var-dtype,\n",
       ".xr-preview,\n",
       ".xr-attrs dt {\n",
       "  white-space: nowrap;\n",
       "  overflow: hidden;\n",
       "  text-overflow: ellipsis;\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-var-name:hover,\n",
       ".xr-var-dims:hover,\n",
       ".xr-var-dtype:hover,\n",
       ".xr-attrs dt:hover {\n",
       "  overflow: visible;\n",
       "  width: auto;\n",
       "  z-index: 1;\n",
       "}\n",
       "\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  display: none;\n",
       "  background-color: var(--xr-background-color) !important;\n",
       "  padding-bottom: 5px !important;\n",
       "}\n",
       "\n",
       ".xr-var-attrs-in:checked ~ .xr-var-attrs,\n",
       ".xr-var-data-in:checked ~ .xr-var-data {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       ".xr-var-data > table {\n",
       "  float: right;\n",
       "}\n",
       "\n",
       ".xr-var-name span,\n",
       ".xr-var-data,\n",
       ".xr-attrs {\n",
       "  padding-left: 25px !important;\n",
       "}\n",
       "\n",
       ".xr-attrs,\n",
       ".xr-var-attrs,\n",
       ".xr-var-data {\n",
       "  grid-column: 1 / -1;\n",
       "}\n",
       "\n",
       "dl.xr-attrs {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  display: grid;\n",
       "  grid-template-columns: 125px auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt, dd {\n",
       "  padding: 0;\n",
       "  margin: 0;\n",
       "  float: left;\n",
       "  padding-right: 10px;\n",
       "  width: auto;\n",
       "}\n",
       "\n",
       ".xr-attrs dt {\n",
       "  font-weight: normal;\n",
       "  grid-column: 1;\n",
       "}\n",
       "\n",
       ".xr-attrs dt:hover span {\n",
       "  display: inline-block;\n",
       "  background: var(--xr-background-color);\n",
       "  padding-right: 10px;\n",
       "}\n",
       "\n",
       ".xr-attrs dd {\n",
       "  grid-column: 2;\n",
       "  white-space: pre-wrap;\n",
       "  word-break: break-all;\n",
       "}\n",
       "\n",
       ".xr-icon-database,\n",
       ".xr-icon-file-text2 {\n",
       "  display: inline-block;\n",
       "  vertical-align: middle;\n",
       "  width: 1em;\n",
       "  height: 1.5em !important;\n",
       "  stroke-width: 0;\n",
       "  stroke: currentColor;\n",
       "  fill: currentColor;\n",
       "}\n",
       "</style><pre class='xr-text-repr-fallback'>&lt;xarray.Dataset&gt;\n",
       "Dimensions:          (chain: 10, draw: 1000, model/obs_dim_0: 200, model/obs_dim_1: 1)\n",
       "Coordinates:\n",
       "  * chain            (chain) int64 0 1 2 3 4 5 6 7 8 9\n",
       "  * draw             (draw) int64 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999\n",
       "  * model/obs_dim_0  (model/obs_dim_0) int64 0 1 2 3 4 5 ... 195 196 197 198 199\n",
       "  * model/obs_dim_1  (model/obs_dim_1) int64 0\n",
       "Data variables:\n",
       "    model/obs        (chain, draw, model/obs_dim_0, model/obs_dim_1) float32 ...\n",
       "Attributes:\n",
       "    created_at:     2020-08-19T12:12:02.008383\n",
       "    arviz_version:  0.9.0</pre><div class='xr-wrap' hidden><div class='xr-header'><div class='xr-obj-type'>xarray.Dataset</div></div><ul class='xr-sections'><li class='xr-section-item'><input id='section-7c46b00d-646f-4410-a108-48f232b7be69' class='xr-section-summary-in' type='checkbox' disabled ><label for='section-7c46b00d-646f-4410-a108-48f232b7be69' class='xr-section-summary'  title='Expand/collapse section'>Dimensions:</label><div class='xr-section-inline-details'><ul class='xr-dim-list'><li><span class='xr-has-index'>chain</span>: 10</li><li><span class='xr-has-index'>draw</span>: 1000</li><li><span class='xr-has-index'>model/obs_dim_0</span>: 200</li><li><span class='xr-has-index'>model/obs_dim_1</span>: 1</li></ul></div><div class='xr-section-details'></div></li><li class='xr-section-item'><input id='section-37f56e16-8169-4329-bd39-033864999c34' class='xr-section-summary-in' type='checkbox'  checked><label for='section-37f56e16-8169-4329-bd39-033864999c34' class='xr-section-summary' >Coordinates: <span>(4)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>chain</span></div><div class='xr-var-dims'>(chain)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 6 7 8 9</div><input id='attrs-0eeccbe3-e46d-4840-a0f6-49500acb6a1f' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-0eeccbe3-e46d-4840-a0f6-49500acb6a1f' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-01b13910-659b-4a75-a610-37543426aaa9' class='xr-var-data-in' type='checkbox'><label for='data-01b13910-659b-4a75-a610-37543426aaa9' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>draw</span></div><div class='xr-var-dims'>(draw)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 995 996 997 998 999</div><input id='attrs-8da08f97-5716-4582-baf1-6ebd580ec713' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-8da08f97-5716-4582-baf1-6ebd580ec713' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-5bf128e0-710d-49f1-9c30-550311cd180d' class='xr-var-data-in' type='checkbox'><label for='data-5bf128e0-710d-49f1-9c30-550311cd180d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2, ..., 997, 998, 999])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>model/obs_dim_0</span></div><div class='xr-var-dims'>(model/obs_dim_0)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0 1 2 3 4 5 ... 195 196 197 198 199</div><input id='attrs-7aa54c95-4fbc-46de-bcfa-0d9c9e543201' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-7aa54c95-4fbc-46de-bcfa-0d9c9e543201' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-3aee3527-352b-43e7-a92e-d2d5e4c9244d' class='xr-var-data-in' type='checkbox'><label for='data-3aee3527-352b-43e7-a92e-d2d5e4c9244d' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,  10,  11,  12,  13,\n",
       "        14,  15,  16,  17,  18,  19,  20,  21,  22,  23,  24,  25,  26,  27,\n",
       "        28,  29,  30,  31,  32,  33,  34,  35,  36,  37,  38,  39,  40,  41,\n",
       "        42,  43,  44,  45,  46,  47,  48,  49,  50,  51,  52,  53,  54,  55,\n",
       "        56,  57,  58,  59,  60,  61,  62,  63,  64,  65,  66,  67,  68,  69,\n",
       "        70,  71,  72,  73,  74,  75,  76,  77,  78,  79,  80,  81,  82,  83,\n",
       "        84,  85,  86,  87,  88,  89,  90,  91,  92,  93,  94,  95,  96,  97,\n",
       "        98,  99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111,\n",
       "       112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125,\n",
       "       126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139,\n",
       "       140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153,\n",
       "       154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167,\n",
       "       168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181,\n",
       "       182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195,\n",
       "       196, 197, 198, 199])</pre></div></li><li class='xr-var-item'><div class='xr-var-name'><span class='xr-has-index'>model/obs_dim_1</span></div><div class='xr-var-dims'>(model/obs_dim_1)</div><div class='xr-var-dtype'>int64</div><div class='xr-var-preview xr-preview'>0</div><input id='attrs-d2809ce2-13fe-4ce1-8b73-d1e6d65795d8' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-d2809ce2-13fe-4ce1-8b73-d1e6d65795d8' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-89ba0ed4-75da-441b-86f4-443a8fea6f33' class='xr-var-data-in' type='checkbox'><label for='data-89ba0ed4-75da-441b-86f4-443a8fea6f33' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([0])</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-252da4c5-4190-4df9-9eb6-0e8f7930fdf9' class='xr-section-summary-in' type='checkbox'  checked><label for='section-252da4c5-4190-4df9-9eb6-0e8f7930fdf9' class='xr-section-summary' >Data variables: <span>(1)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><ul class='xr-var-list'><li class='xr-var-item'><div class='xr-var-name'><span>model/obs</span></div><div class='xr-var-dims'>(chain, draw, model/obs_dim_0, model/obs_dim_1)</div><div class='xr-var-dtype'>float32</div><div class='xr-var-preview xr-preview'>26.57001 26.04135 ... -14.317561</div><input id='attrs-bc8ca1ce-a73b-45e5-8938-8eff592dd95b' class='xr-var-attrs-in' type='checkbox' disabled><label for='attrs-bc8ca1ce-a73b-45e5-8938-8eff592dd95b' title='Show/Hide attributes'><svg class='icon xr-icon-file-text2'><use xlink:href='#icon-file-text2'></use></svg></label><input id='data-aa3156b7-f141-4a52-bce8-aab0fab7d89b' class='xr-var-data-in' type='checkbox'><label for='data-aa3156b7-f141-4a52-bce8-aab0fab7d89b' title='Show/Hide data repr'><svg class='icon xr-icon-database'><use xlink:href='#icon-database'></use></svg></label><div class='xr-var-attrs'><dl class='xr-attrs'></dl></div><div class='xr-var-data'><pre>array([[[[ 2.65700092e+01],\n",
       "         [ 2.60413494e+01],\n",
       "         [ 2.57281590e+01],\n",
       "         ...,\n",
       "         [-4.75241995e+00],\n",
       "         [-4.78487253e+00],\n",
       "         [-4.75552654e+00]],\n",
       "\n",
       "        [[ 3.16064491e+01],\n",
       "         [ 3.10987301e+01],\n",
       "         [ 3.04416885e+01],\n",
       "         ...,\n",
       "         [-5.26556778e+00],\n",
       "         [-5.20179415e+00],\n",
       "         [-5.47270155e+00]],\n",
       "\n",
       "        [[ 4.52943230e+01],\n",
       "         [ 4.45980377e+01],\n",
       "         [ 4.39933929e+01],\n",
       "         ...,\n",
       "...\n",
       "         ...,\n",
       "         [-5.59512615e+00],\n",
       "         [-5.61213923e+00],\n",
       "         [-5.73862267e+00]],\n",
       "\n",
       "        [[ 2.81977844e+00],\n",
       "         [ 2.81224990e+00],\n",
       "         [ 3.02726460e+00],\n",
       "         ...,\n",
       "         [-5.47826385e+00],\n",
       "         [-5.42433500e+00],\n",
       "         [-5.45992947e+00]],\n",
       "\n",
       "        [[ 3.89422917e+00],\n",
       "         [ 3.80268312e+00],\n",
       "         [ 3.86203289e+00],\n",
       "         ...,\n",
       "         [-1.39646444e+01],\n",
       "         [-1.41936607e+01],\n",
       "         [-1.43175611e+01]]]], dtype=float32)</pre></div></li></ul></div></li><li class='xr-section-item'><input id='section-06fb4778-5e93-4a49-b46d-359b4e3e7aa4' class='xr-section-summary-in' type='checkbox'  checked><label for='section-06fb4778-5e93-4a49-b46d-359b4e3e7aa4' class='xr-section-summary' >Attributes: <span>(2)</span></label><div class='xr-section-inline-details'></div><div class='xr-section-details'><dl class='xr-attrs'><dt><span>created_at :</span></dt><dd>2020-08-19T12:12:02.008383</dd><dt><span>arviz_version :</span></dt><dd>0.9.0</dd></dl></div></li></ul></div></div>"
      ],
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:          (chain: 10, draw: 1000, model/obs_dim_0: 200, model/obs_dim_1: 1)\n",
       "Coordinates:\n",
       "  * chain            (chain) int64 0 1 2 3 4 5 6 7 8 9\n",
       "  * draw             (draw) int64 0 1 2 3 4 5 6 ... 993 994 995 996 997 998 999\n",
       "  * model/obs_dim_0  (model/obs_dim_0) int64 0 1 2 3 4 5 ... 195 196 197 198 199\n",
       "  * model/obs_dim_1  (model/obs_dim_1) int64 0\n",
       "Data variables:\n",
       "    model/obs        (chain, draw, model/obs_dim_0, model/obs_dim_1) float32 ...\n",
       "Attributes:\n",
       "    created_at:     2020-08-19T12:12:02.008383\n",
       "    arviz_version:  0.9.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "draws_posterior = pm.sample_posterior_predictive(model(x=x_test, y=np.zeros_like(x_test)), trace, inplace=False)\n",
    "draws_posterior.posterior_predictive"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictive mean and standard deviation can be obtained by averaging over chains (axis `0`) and predictive samples (axis `1`) for each of the 200 data points in `x_test` (axis `2`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictive_samples = draws_posterior.posterior_predictive.data_vars['model/obs'].values\n",
    "\n",
    "m = np.mean(predictive_samples, axis=(0, 1)).flatten()\n",
    "s = np.std(predictive_samples, axis=(0, 1)).flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These statistics can be used to plot model predictions and their variances (together with function `f` and the noisy training data). One can clearly see a higher predictive variance (= higher uncertainty) in regions outside the training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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z0SWX2NIkewuNtvCllCuBWtO6SavTzrG6XgqnEB9utE3entstttHFUZTCbx7YC6N0Jvb89x9+MosH7vsPjz/8IACPPPYE7dt3qLGP6264kQP79zFkQF/8/f257vqbmH77HXw5+1sefuC/5ObmYDKZuP3Oe+jWvXpRlymXXsY9d97GB++9w5fffGdLYRwVFUVi/wHVFHhtDB8xkjdmvsqwgYm20owTz7+AO2+9xevcOaDSIzdpVh1I57NVh3lwXJdGT94G6LUM6RDlJMkU3oK70yOXmS0UlZrdNp4n2LRxI489/AB/LFnW4D5UemRFvenfJoIAnXNW3qoEagpn4M0GpjN4feYrXHvV5Tz93POeFsUuSuE3YXR+Gga1j2TT0Szyissa1ZdKoKZwBk39EvrvAw+xfc9+BtcyB+FJlMJv4lRM3q4+0LjJW5VArenizh9ydQU5j4Z8b0rhN3Fsk7f70hp9Y6uJ26aHwWAgIyPDbUq/scVPFFaklGRkZGAwGOp1nPOyaym8lnM6RzNr1WH2nMqja1xIg/spNVkIUAnUmhQJCQkkJyeT5qbl/6Umi1L6DqDz06CpI7LOYDCQkJBQr36Vwm8GJLaJ4LsNx/hnb3qjFL6auG16+Pv7065dO7eNt+ZABgUlDS9g3lwY3CGSQL3z1bNy6TQDdH4aBjth8la5dBSNRWVd9SxK4TcTRnRu/OStKwqkK5oPUkrK1DXkUZTCbybEhxnpGB3UqMlbZeErGoOy7j2PUvjNiHM6R3Mqt4Q9pxxfOl6ZEmWdKRqBekL0PErhNyP6tQknQKfln70Nq4alLDRFY1CT/p5HKfxmhM5Pw5AODZ+8VRaaojGo68fzKIXfzBjRiJW3yoevaAxK4XsepfCbGS3DjLSPCmTV/vrXvC01qXw6ioajXIKeRyn8ZsiwjlGcyCnmUEZBvY6TUvlhFQ1HWfieRyn8Zkj/thHotBpW7a+/W0dZaYqGoq4dz6MUfjPEqNPSt00Y6w9l1tvqUlaaoqGoa8fzKIXfTBnWMYqiMjP/Hs2q13Fq4lbRUJTC9zxOUfhCiFlCiFQhxPYa9o8UQuRUKnL+lDPGVTSczrHBRAXpWHmgfjH56qZVNJRSc9MubegLOMvC/xw4r442K6SUvcv/nnPSuIoGohGCoR2i2J2SR0Z+icPHqdW2ioZgMluwqEvH4zhF4Usp/wFU1XAfY0iHSIB6xeQrC1/RENSErXfgTh/+YCHEFiHE70KIHjU1EkJMF0IkCSGS3FWUobkSGaSna1wwqw6kO1yUQvnwFQ1BGQregbsU/iagjZSyF/B/wC81NZRSfiSlTJRSJkZHR7tJvObLsI5RpOeXstfBhGrKUlM0BKXwvQO3KHwpZa6UMr/89ULAXwgR5Y6xFbXTp3U4Rn+twzH56sZVNAQ19+MduEXhCyHihLAWaBRCDCgft+GVOBROQ+enYUC7CDYeyaK4rO4oCqXwFQ1BPRl6B84Ky/wWWAN0EUIkCyFuEkLcJoS4rbzJVGC7EGIL8DZwhVRJWbyGwe0jKTVb2ORATL7ZIpUfX1FvlKHgHTilSq6U8so69r8DvOOMsRTOp0N0IFFBOtYezGRIh7o9bSUmC/5atWZP4ThK4XsH6q5VIIRgUPtIdp3MJbuwtM72JQ64fhSKyiiXjnegFL4CgEHtIpES1h+uezmFmoBT1Bdl4XsHSuErAIgLNdA2MoC1B5XCVzgfpfC9A6XwFTYGtY/kaGYhJ7KLam3nSDSPwrlYLL4b42AyWzD7sPxNCaXwFTb6t41ACFh3qHYrX1n47iM9v4RV+9PZfdKxhXHeiPLfew9K4StshBr96d4ihHWHMmotZagmbd2DxSLZezKPolIzJ7KLGlR43htQ7hzvQSl8RRUGtY8kPb+U/Wn5NbZRFr57OJ5dRGHp6R/Xfak1fyfejFL43oNS+Ioq9GkVhs5PU+vkbanJ4tM+ZV/AbJEcSq9aczgzv5ScIt+z8pWB4D0oha+ogsFfS59WYSQdzsRUi+9V+WVdy4nsIruW8dGMQg9I0ziUwvcelMJXVGNguwgKSs1sP5FbY5uSMnUTuwqLRXI4o8DuvtS8YgpLTW6WqHEol473oBS+ohrdW4YQbPBj7cGa89uVmNTEras4kVNU4w+qlHA43besfPU06D0oha+ohp9GQ/+2EWw+ll2jNVmsLHyXYDJbOJhm37qv4GRukU+thVBRXd6DUvgKuwxqF4HJItl0NNvu/mJl4buEwxmFdbpALBZqdPl4I8rC9x6UwlfYpV1UIDHB+hrdOkWlSuE7m6JSM0czHVPkJ7KLfCJNtZRS+fC9CKXwFXapyKC552Se3QyahUrhO519qXlYKunGpfPnMm1sIuN6tmDa2ESWzp9r22exwMmcYg9IWT9KzRZU5QvvQSl8RY0ktglHgl23TlGZqdbVuIr6kVVQSmpuie390vlzeePpB0hNSUZKSWpKMm88/UAVpV9XziNvQFn33oVS+IoaaRlmpEWowW4lLItFxVc7CylltSLys96cQUlxVYVeUlzErDdn2N7nFZu8Pt2CUvjehVL4ilrp1zqcPafy7CoW5dZxDqdyS8grrhoNlXbyOAC6ll2JGH8X0VOeQmMMsW2vwNvdOsoo8C6cVdN2lhAiVQixvYb9QgjxthBivxBiqxCirzPGVbievm3CkRI2H8uutq9Ihds1GotFcsBO3qLouHiM7ROJm/Yygd3PwdCmF7FXvkh0my7Aaf9+lxahtG3bltmzZ7tbdIdQFr534SwL/3PgvFr2TwA6lf9NB9530rgKF9Mq3EhUkI6Ndtw6RT624tMbOZFTVC3iaen8uZTqw4i68CFKUw+R/O61pM19Dv/wlnS8+rlq/v0jR44wffp0r1T6ysL3LpxVxPwfIUTbWppMBr6U1lm+tUKIMCFECyllijPGVzSMXVs38cvXn5CSfAQpJd3O7se5ky+lU/ezbW2EEPRrHc6S3akUlpoI0J2+ZJRLp3FY7CRIm/fNLN5/+Wm00e0o+PpByrJPgKkMeWovRRt/5vjAy3nz/Y+r+fcLCwt5/PHHmTZtmjtPoU6agoVvNptZseg3Vv/1J8mHD+Cv03NWv4FcduOdhISFe1q8euEuH348cKzS++TybdUQQkwXQiQJIZLS0tLcIlxzJeXoYTauXo4xIBCdXs/CH7/mP1dNIiuj6ufet004Zotka3JOle1K4TeO49nVUyh88X+vYDaZQErMRXlgss6dlBQXkbbiO8qyUggfMx1E9Vv36NGjbpG7PpSaff8a+e27z3nhgdv4d90KwiIi0Wg0LPjhK3R6vadFqzdOsfCdiZTyI+AjgMTERBX352T2bPuXY4cPMPaCqYwYfwHDxp2PTme9cAvyctmatJbwyGjAqmT0BiPtogIJD/Bn49EsBrWPtPWlFl81HCklxzKtOXHKSks5uHcnXXr2psAsaHHDW5gLskmd81TVg8xlZPzxf8Rd+SKB3UZQsHN5ld2tW7d2k/SO48tJ9kxlZfj5+zNhylVERscydOxENBrrD21xUSEGYwClJcV89d5rXDn9PwQEBnlY4rpxl4V/HGhV6X1C+TaFG9m/axuPTL+Cr957jdKSYvz8/W3KHiAwOITBo8YB8Pcf87j7yokU5OWiEYI+rcLZcTy3Sl4Us0Uqpd9A0vNLKSw1Y7FYmPnEvTxyy+UU5OXS4vy78Y9IIHPxB3aPKzm6lZx1PxEy+FJA2LYbjEZeeOEFN0nvOL7qw9+yYTXTLxlNRtop9AYjw8dNsil7AIMxAIBdWzYy57P3eHT6FdXcbN6IuxT+r8C15dE6g4Ac5b93L7nZmTx11/UYA4J45dM56PSGWtsHh0Vw9OA+nr//VsxmM33bhFFqtrDtRFW3jrfHgXsrx7Ks1v2z/7mRvxb8RH5uDrfdfjt+7QZQkPQLpqwTlVqLKsdmL/8MWVqMsdMgADQaLQ/873Wuuuoqd4nvEGU+Wrw8JfkIz917M0hZxSCyR68BQ3n81Q/YuTmJt//3iNcvRnRWWOa3wBqgixAiWQhxkxDiNiHEbeVNFgIHgf3Ax8AdzhhX4RhSSl5+9G6yM9J4+q1PiW3Zqs5j+g4azj1PvETSqmX88Nl7dI4JJtjgx6Yj2VXa5RarSJ36kldcRmZ+KbPemsHqv/4o3yoQfS6mLOsEBRvnERIWjhCCmBYJXHD5tegNxko9SNLmvUTgWWPRG4w8NONtzplwMZkF1VNgeBJfnLA1m0y8cP+tWCxmnnvnC4JDw+o8ZsT4C7j69v+y6Jfv+X3uN64XshE4K0rnyjr2S+BOZ4ylqD//rl3B+n+WcudjL9ClZ2+Hj5swdRpJq5bx5TuvMnDEWHonhLHhSCZlZgv+WqutoCz8+nM0s5CCvFy+/+Qd27bAnqPRRbcl7ZcZFOfnIA1GHn7pHcZMmgJAj74DmPXmDFJTkhFCgzk3naJ9q5n+1BuMmXQRYF3AFRnkPROJvujO+eHz99mzfTNPvPYhCW07OHzcNXc8wI5/N/D1+69z7oWX4q/TuVDKhuN1k7YK59N38Ahe//IXevQZUK/jhBDc89TL7NyykX/XraTf6MtYsT+dnSm59EoIA5SFX1+Ky8ycyi3mn0W/YbGUz39o/QkbPo2SE3sp3LMKOJ1GoULhj5k0xfYa4IuP3uXPZPBrP9C2LTWvmK6WYDSaqi4gT+FrRXIsFgvr/1nK8HPP55zzJtfrWI1GwwPPv4lGq/VaZQ9K4Td58nKyCQ4N46x+gxp0fFhEFJ8vXI3BGIDJbMHor2XjkSybwi8zWSguM2Pw1zpR6qaFlBIhBEWlZval5rH417m8++ITtv1BPcfgFxJDxsK3qhx3ZhqFylw3/U5O/rGbNQczmNAzDiEEJrMkq7DUa6x8X4vQ0Wg0vDrrR4obOPka08IaaS6lJDsz3Rbt5k2oXDpNmMP7d3PFqN6V/MQNoyIiYfeWJLpH69h2PAdLpcm4XOXWqRGzRbL6QAbL9qSy+kA6qbklvPXsw6cjOoSGkIFTKDmxl+IjW6ocGx1nd6mKjQGtQtg1/1PmfPedbdupShk3PY0vuXSOHtxHbnYWWj8/AoOCG9XXjIfu4JGbL8fshWsQlMJvwnz21kv4+fvTs2/9XDn2OHpwH/ddcyGFW34nr9jEoUoVl85M/KU4zaH0fIpKzZjNEilh+6b1FBWezp0T0GUo/uEtyFn7Q5Xj9AYjN977aK19D+gYTfGhjXz3/iuUlloVfWpecZUfY0/iKy4dKSWvPHo3D9441SlRNkPHnMfBvTtZ+tuPTpDOuSiF30TZs30zq//6g8tuuIOQsIhG99e6fSf6DjmHNT9/BmXFbEnOtu3LKVIWvj1O5RZzJKNqwfEv3nmlSjx36KCplGUco2jfWjQarS0y575nZ1bx2dsjUO9P/ym3kZ+Rwvw5XwFgMkuyveT78BULP2nlMvZs38zkq25EiMbPf4wYfyGdepzN7A/esK6a9iKUwm+ifP/J/xEUEsrF19zitD6vuf1+crIy0O9bypZjp+PxcwrLvD7+2N3sPZXHtuScKtWetm9cx+Z1Kxk18WL0BiOGdn3RxXYgZ91c9AYDD814m0XbU5i9JMmm7KOD9fRtE86orjH0bROOn7aqQrpo0gT0Cd359pN3MZVZFX1qnnekTPYFH76Ukq8/eIOYFvGce+GlTulTCMFV0+/lxLHD/P3nb07p01kohd8EyUpPY82yRUy+8kanLvfu2XcAvQcO4/jKH0nOyCUj3+pGMFukitapRE5hGUfPsOwB5nz2HiFhEdz7zKvc9+xMokZMw5SXTmDmvmoWvZ9W0K9NOL1ahRERqEOrEUQE6jgrPrRKnz3iQ4kcNIXstBQm9G7FtLGJzJ79jcd/gKWUPuHS2Zq0hp2bN3D5TXc5NbpmyOjzaN2+E4t++d5pfToDFaXTBAmPimbW/JUEBjdu8skel95wOy88eDtl6cfYktyB0V1jAMguLCXU6O/08XyRval5drf3HzaKxKEjMRgDaD/oPLSZu7gsMYFxd66r0k6rsaayCA2o/nlGBulpFRFgy8Pz98KfKcnNIKjP+eRvW0JqSjKvPvFfWkcYueWG65x/cg7iK7Vst25YTVhEJOMvvsKp/Wo0Gp595wtb5I63IDxtCdRGYmKiTEpKqvdxOUVlbDiU6QKJvJ+KEEBXYbFYKCkq4vnFB4kK0nPf2M6A1fXQq1WYy8b1FU5kF7HzRG6d7T5deYhNR7OYObUXRl3VkNZuLUOIDzPWcKQ1ln/1gXQsFpg2NpEcTRBxV88kff7rFOz4C4CWCa04fsxz2TNzi8tYf9A37sGK0GVXYbFYqszbOMLgDpEE6htmjwshNkopE+3tUy6dJsaPn7/P47dPo7TENX5cjUaDMTCQs+JD2XXkFMXlydSyCks97kbwNMVl5mq1acGahXThD19TVGCNbMotKmPD4UyGdIispuzDA/1rVfYABn8tsSHWXEhpJ49Tcnw3ppxT6OO72dqkHE/26PfhC/77iu/Dlcp++6b1XDdhEMlHDrpsjPqgFH4Twmw2M++bWZQUFdWZHK0xSClZ8tLNnPrjHW6Zfivjerbg8lH9mPXFVy4b0xfYdyofk7m6kl386w+88cwDHDu8H4AV+9MxWSSjusRUaScEdI0LcWistpGBwOlY/YJd/2DKPmnbHx0XT3ah56J1vN1/X1xUyNXj+vPL7E9cOk7LVm1JP5nCr9985tJxHEUp/CbEhhVLOXUimQuvvMGl4wghiIwIp3DPKkqCWyKlJDUlmbvvuM0ry+y5g4ISE6dyqz9VSSmZ//0XdO7Ri849emGRkn/2ptE1LpiWZ1jyLUKNDj/GB+r9CAvw58Z7H0VvMFKw6x+C+04EQKv148Z7H+WkHXnchbeHZP79x6/kZmfSvksPl44TER3DsHMnsuS3H21rJTyJUvhNiD9++pawyCiGjK6tvLBzOLx3N5hNWIpyqUjfW1RUxOOPP+7ysb2RwxkFdrdv37SOIwf2csEV17F0/lyuu/ZaMgpK2TrndZbOn2trp9FAu6jAeo3ZIszImElTuO/ZmYRry5CmUgzx3QgIDGLkhItIzSvx2CIsb3fpLPzxa1q169jglCP1YdxFV5CXk8XaZYtcPlZdKIXfRMhKT2Pt34s598JL8fN3fbRMVkYqmoBQCnavxD+mnW27N5bZczUVCdHssWjeHAzGACTwxtMPYGrVF3NRLinrF/DG0w/YlH5ciLGaP78uYoL1aDTWxGqzlyQxdfRAghMnk5ebzeZ1KykzWcgq9EzKZG926Rzat4udm5OYOPVqlwY4VNB38AiiYluwaJ7nQzSVwm8i+Pn7c/1dDzNx6tVuGS86Lh5ZVoIpMxl9XEfb9viEunPtNzWOZBRisWPQSilJPZHM8HPP5+v3XqdM+BPQaRAF2/8Cs8mWEROgVUTtE7X28NdqiAk+PVfTv10Exo4DCIqIISX5CIDH3Dre7NJZPG8OWj8/xl441S3jabVabvnvk0y67Fq3jFcbKg6/iRAcGsYVt9zttvFuvPdRXn/qfgLOuQ59y67kb12E3mDkvkefdpsM3kCJyczx7OqLrMA61/HyJ3MoKy3l/L5tCEqcjND6k7/19KN92snjhAf6E2xo2FNZi1ADJ3OsSj0uxECbmDDaPjibSReeZe2/3K3j7pTJ3qzwL7zyBjr36EVYRJTbxhw96RK3jVUbysJvAiQfOchfC352a03NMZOm8N/nXiPAoEffqgcxbbty37MzGTK+fnnEfZ2jNVj3gC001l+nIzounqCzx1F8fBdl6afdXtFx8bQKD2jw+BGBOvT+p2/jge0iOJJdwqncYgoLrFFDGW6uhGWxSMq8WOHHxbdm5ISL3D7uyeNH+fHzDzwaLqsUfhPgj7nf8Mpjd1NcZN/SdBVjJk3h0XvvJGf19/QcfTGz3pzBkI7RtG7TpllE65jMFpKz7f/IZmemc+nwnjYf/QV3PoMuqjX5W05b93qDkVvvf5zo4IbnrxdC0CL0tDuof1troryn77mBp+++HqDG+QVX4c3W/bxvZjU6XXhD2bRmBR+++gy7t/3rkfHBeTVtzxNC7BFC7BdCPGJn//VCiDQhxObyv5udMa7Cuopv+e+/0HfwCELDI90+ftvYUPKS5rFq0a+kplgX+xw7epTp06c3eaV/IrsYs524e4Dlv/9CYUE+7bt0B6Awpgd+WAjMPlglI+YN113T6InDlmGn/fgRgTo6xQRRGtqGLetXkXoimbT8ErcWE/fWCdvSkmJmvTWDlUsWemT8c867EL3ByJ8/f1d3YxfRaIUvhNAC7wITgO7AlUKI7naafi+l7F3+59rVDs2InZuTOHUimdHne8ZHaNAbMLToROnJ/VSEZwIUFhY26RBNKSXHsmp+olo87wc6dO1Ju07dKCw1kXQkiyGdYpj9xypbRsxzL5xSRVk3lACdHyGV8hgNaBeBucMw6wK5+XMxmyXp+e6LAfdWC3/d30sozM+rM+20qwgMCmbI6PNYsWi+LbOpu3GGhT8A2C+lPCilLAW+A5qXI9eDLFv4Mzq9wS2x9zVhNpuRphL8wltU2d6UQzTT80spKrVvyR49uI+9O7bY0u1uOJxFqcnC8E5VS97FBBvQ+zmnNGRciIGl8+cybWwiL189HL+QaPzDW/DZWzOYNjaRWZ+7bxW0t8bgL13wExFRMfQeOMxjMpxz3oXkZmeyZcNqj4zvDIUfDxyr9D65fNuZTBFCbBVC/CiEqDF2TwgxXQiRJIRISktLc4J4TZtD+3YxeNQ4p6ZBri8hshBtaAxnpkds3bq1hyRyPbX5xZf//gtCCEZOvAiAFfvSSAg30jay6uRsYyZrz2TZwrm88fQDpKYkYy7MofjwZgJ6jAYgNSWZZx/+D19+9bXTxquNYi906eTlZLP+7yWMnHARWq3n6i8nDh1JaHgExw7t98j47grL/A34VkpZIoS4FfgCGG2voZTyI+AjsGbLdJN8Pstrn//s9snaM7nprvt4Z/YvlGWfwpSdAoDBaOSFF17wqFyuwmKRpNXiIjnnvMlExbYkMjqWY5mFHM4o5Mr+rar46oMMfnbTHzeUp598skqUVsGuvwkfeQP525dizj5JSXERN95wPVqNYNq0aU4b1x7eaOGnJB8hLqG1x8Mj9QYj3/612am59+uDMxT+caCyxZ5Qvs2GlDKj0ttPgFecMG6zpyLtqjGgfkvync2YSVPYWRTClqJwjr93HRFB1ugTVysWT5FeUFLjZC1Amw6dadPBmjZ61YF0/DSCge2rTqgnhNd/oVVtnOk+K9y7lsjxdxHS70Kyln4EWF1v06dPB3Dpd+ONk7ade/Ri1vyVXpHRtULZm81mtz9tOMOlswHoJIRoJ4TQAVcAv1ZuIISo7Ny9ENjlhHGbNWWlpVwzrj+/z/3G06IAcMlYq1/03vfmMXtJEiMmXExusXfUVnU2qbk1W/drli1i3d+LAWvY5tqDmfRuFUZQpaRoWo0gLsS52UzPdJ/J0kKKDiRhaNsbd0+me9ukbWlpiS1xmTtSKdSFlJJHbrmCt559yO1jN1rhSylNwF3An1gV+Rwp5Q4hxHNCiAvLm90jhNghhNgC3ANc39hxmzub168iNeU44ZHuWy1YGy3DDJg2/8brN4ymIM9aACQtz/PZAZ2NlLVHvHzxzit889HbAGw7nkN+iYkhHapa91FBevy0zl0C88ILLxAQUHVOoGDX32h0AUBVq9aVk+neWNrwnz9/49LhPTlx9LCnRQGsPzphEZGsXLLQ7dE6TrnqpJQLpZSdpZQdpJQvlG97Skr5a/nrR6WUPaSUvaSUo6SUu50xbnNm1ZKFGAMC6Tt4hKdFAawX8Vl9E7GYSllVnhWwKSr83GKT3Zz3ACeOHubA7u0MP/d8AFYdyCDU6E+PllXr0MaGNnyhVU1MmzaNjz76iIRWrRFCEBwaTvHBjWj0AfiFVY2ecuVkeonJUuPKY0+xcslCAgKDiEvwniCCEeMvIC8ni3/XrXTruGqlrQ9iNptZ9dfvDBgxxqWFTurLqOFD0QZF8OeCeQDkF5tsFbGaCpm1pClYsXg+AMPHnU9uURnbknMY1D4CbaU8NlqtICrQ+QofrEr/yOHDLNt9ip9W7+Kh51+j5GASgWeNtbXRG4w897/nXTI+eN+EbVFhAUkrlzF0zIR6lxl0JYlDRxIQGMQ/f/5ad2Mn4j2fgMJhdm1OIjsjnWFjJ3pMhvBAf7q2CCagUkrf7i1DCew8hB3r/6Go0JofvqlZ+ZkFNZ/PikXz6dKzN7EtW7HuUCZmKRnSoarLLTpI79JEZhqNIDbE+oMyZtIUzuvfhaCeowAIDA7hvmdnujRSxdtCMpNWLqOkuMj21OUt6PQGBo0cx5plf2I2u+8zUwrfBwmPimHq9bfRf/gYj8nQMSaYhPAAOsScjv83+GvpNngs5tISNqywFtOuLXzR1zBbJDlF9n2uhQX5ZKanMaxcsaw+kE7byIBq9Wkjg1wfjlc5t86VkycQGtWCqA5nM3rixYyZNMWluXW87YluxeIFhEVE0tMNhU7qy6TLr+W6ux/GbDa5bUyVHtkHiW/TjlsffMZj4xt1WkLLl/LHBOsJMviRX2y9aEeMGM6+A3cT360fANmFpZjMFqdPUnqCrMLSGv3TAYFBfL14AyZTGUczCzmWVcS0AdV9xqFG1xenCTX6E6DXUlhixk+roV+bcNZe9gK3XtEXgKyCMorLzBj8nR8SWORlCv+Sa25h6JjzPLrYqibO6jfILRW3KuP7d2Ez4+Txo2xetxKzyX1WwZnEVMruKISwFdQG6NU6kuBe4zlSaLUlLBbcnp7XVdTmv5dSotFo0On0rC6Pve/fLqJKGz+tIEDnHhurspU/oF0EpRbBlmM5WMp/sSpy6DubYi/z4Xc9uy/nnOe9mV6yMtL4a/5PbhtPKXwf44+fvuXhmy8jLzfbYzLEnBFDHh2sR6u1+qVjQwxE6iXz53zJ3h1bgNrj1n2JmsIx83NzmDY2kRWLF9QYew/use4raBF6+jvqHBNMmNGfD59/wJYy2VWVsLzJpbP891/YtnGtp8WolRWL5jPj4Ts4enCfW8ZTCt/HWLX0d3r2G+jWaj2V8ffTVFNcWo0gOshq9S+dP5eTSYvYPvdtHrjxUpbOn0t6geeKaTuL4jIzhSX2ldmGlctIO3mciKiYGmPvwb0K3+CvJTzQOp5GI4i1ZJBV5sfa5Yu4cnRf5v34PXkuWBjnLQrfYrHw/stP88vsTz0tSq0MGjkOgDXL/nTLeErh+xApyUc4vG83Q0Z5LjNmsMG+S6JFqDVb4xtPP0DG9uUY2vahuLiE15+6n0XzfvR5t05t8q9dvoiwiEi6nt2X1TXE3oN7FT6cdussnT+X1V/MIKCz1V+cfuoEbzz9AB/N+tKp45WZLTWuUXA3+3ZsITPtlE2heisxLeLp1P1sVv+lFL7iDNYuty7Z9+RFHFJD7dWIQB2fvTWDkuIiSo7twND6bKSpxFp04s0ZPh+emVGDO8dUVsb6FUsZMGIshWUWtibnMKhd1dj7CkLcrPBjgvVoNDDrzRnkH9mGJjAMobP+CJQUF/HqC884NbeMt1j3AGuWL0Kj0TBwhOci2Rxl8Khx7NqSRFaG67MDK4XvQ2xet5JW7TsR36adx2QIqcHCF0KQmlKeM09WnrgTpJ08Tlq+77p1pJQ1Ttju+Hc9+bk5DBo5rsbYe4AAnRZ/N0cq+Wk1RAXpSTtp/V6K9qzG2GEAFbl1UlOOk1XoPLeON03Yrl2+mO69+xMSFlF3Yw8zeNR5SCnZvmm9y8dSCt+HeOqNT3jxA8+WDQyuwcIHiE84nTS1+Nh2dC26oAkMIzounjKThaxC33Tr5JXUnE4hNCKSCy6/jsQhI1m1vzz23k4mzNo+N1cSG2IgOs5anqJg1z8E9xqPrmVXwFpA3ZnROt5i4Rfk5ZJ28gSDRp7raVEcokPXHnyzdJNbFocphe9DaP38iIv3XD4QP63AqKs5nnnGiy+iN1iVXfHhTcRc+gwRQ6/gxnsfBeCUj0brZNXiv2/bsSv3PPUyaSWCY1lFdq17sOa/9wRRQXpuvu8x9AYjZelH0QSEED7qevQGIzfe+yin8oqdVu/WW2LwA4NDmPPPNiZfdaOnRXEIIQTRcS3dMpZS+D7CZ2+9xFfvveZRGeqyUq++ehrPvvo2MS0SwFQK6QeJ6TeeURMvBiA1r9gn3To1uT0y0k6xZ9u/WCwWW+z9gLb2XQg1TXa7Gq1GcOVVV3HfszOJaZFA4a5/0EW1YczU6xgzaQpms6xxfqK+1FTy0RNotVoMRudVFHM1GWmnePru620r1F2FUvg+gNlsZsEPX3L86CGPyuGI0rrhuquZvSSJRdtTuOmyyRz9/QOe+I+16IbJLMn0MbeOlLJGV9TS337krismcPJEMmsPZtKrVViNlvyZMfnuJCZEz5hJU5i9JIn333iV/B3LWPj1B7Yye86KyS/0AoVfVFjALZPPYdXS3z0tSr0ICQ1n8/pVrFi8wKXjKIXvA+zaspGcrEwGe9gn6YjSigjQUZGUsFerUITGj43/LOKqMf0Y17MFZ3ftxOzZnp2HqA+5xaYaq1utXb6Y9l16cMoSTH6JiaF2Yu8BdH4al6QxcJSoQD1+5QvjooP1dB0wErCGk4J1QZnJ3LgJVyklRWWeW/1dwb9rV3B4/x4CAoM9LUq98NfpGDB8NGuXL7KthnYFSuH7AGuXL0Lr50fi0FEelSOgFv99BX5aDWEBOpbOn8ttkwajDY3FYiol7eRxpJSkHD/G9OnTfUbpZ9dg3edmZ7Lj3/UMHjWO1QcyCDH42Y29B8/57yvQaAQxwadX3sbqy/CPacfHb77EtLGJLP51Lun5jXvy8pY8+GuWLyIwOISz+g30tCj1ZvCo88jKSGP31k0uG0MpfB9g7fJFnNVvEIHBIR6Vw9E8MCv/+IU3nn6A1JRkTLmpCJ0R4X86csUdZfacRU0Lrtb9sxSLxcLZQ0azNTmHwe0j7cbeQ82hrO4krjzVwtL5c/nz7UcwdhiANJWRmpLMSw/fSbd28Y36EfYG/73FYmHd8sX0HzYKP3/PREU1hgHDR6PRallbXiLTFSiF7+WUlpbQoWtP28Snp/DTCnR+jl0uM194hpLiIgCK9q3F2K4f7iyz5ywsFklODRO2SSuXEREdS4YhocbY+wpCja5PiVwX4QH+6P01zHpzBkUZJ/ALjqDyd5KdldmoJ69CL4jQ2bN9M1kZaV6/urYmgkJCmTh1mksjdpyi8IUQ5wkh9ggh9gshHrGzXy+E+L58/zohRFtnjNsc0On0PPrKe0ycOs2jcgTWY9Ix+dgx22tzbhr6+G4Edj+nSptWrVqdeZjXkVNUVmPI4n+fe42XPv6O1Qcza4y9B9BorMrW0wghiA0x2BZhlZw8QMubP8A/pr2tTWOevIpKPe+/NxiMjL1wKv2Hjfa0KA3mP0+9wgWXX+ey/hut8IUQWuBdYALQHbhSCNH9jGY3AVlSyo7AG8DLjR23uZB28oSnRQDAWI9JxzNrpprzM4g87260ITGAtczeA48/40zxXEJt+XP0BiN+kW1qjb0Ha/4cb6kF0CL09CKsor2r8QuLq/ZD3NAnL2+I0GnXuRsPz3iHkLBwT4vSKEqKi6oYTc7EGVfiAGC/lPKglLIU+A44MwH1ZOCL8tc/AmOEEK6r89ZEKMjL5ZrxA/j247c9LUq9LPwXXngBY6UY6MI9q7CUFaNv2ZmYFgnc9+xMhoz33hzlFdQUjvnj5x/w7cdvs/pARq2x9wARLqpf2xCCDf7c/uAT6A1GLMX55O/8m5Lju6q0SWjgk5enFX5udiZH9u9xam4gT3HPledzz113uKRvZyj8eKDyz1Fy+Ta7baSUJiAHsBvDJoSYLoRIEkIkpaU1LJnQg/+9l7eee6hBx3oTSauWYTaZOKuv5yMOAh2I0Klg2rRpfPzxR8S2TEAIQUSAP+bNv1K4eyVvfPkLYyZNIaugjBIvq39aGZPZQq6dcoZSSuZ98ynb/13P2kMZtcbeg3tKGtaH66+5mvuenUlwaDjFB5MoPrQJTaDVItYbjPz30acb1K+nV9ku/30eN08+x+NrVZzB7Y88x4xXXnVJ397xrFkJKeVHUspEKWVidHR0g/ooyM9n+e/zMJU5P9+3O1mzfDEhYRF0653oaVFqTalgj2nTprFk/XYWbU9h9pIkzp1knXReuuj0gphTOd6baiGrsAx7xuLh/bs5efwYrXoNJ6+45th7sE50B3twwZU9YkMMjJk0hZ9W7+L266/E0PpsMJcRHRfPfc/OZMC5F9a7z+Iyc41rFdzF2uWLiG/TnoQ27etu7OX0HjiMLl26uqRvZyj840Dl58CE8m122wgh/IBQIMMJY9vlvInnk5+bw45/XZ99zlWYTSbW/7OUASNGe0U9zoaU5qtcCvHcwX3wC2/JX5UUfkpOkVNkcwU1uXPWLLMuVsqP7VVr7D1Y/ffe5rk06rSElk8in3fBJXQbNAZLcT7PvfsVYyZNobDETG49C6Pkl3h2wraooIDN61b5TLI0T+IMhb8B6CSEaCeE0AFXAL+e0eZXoGLqeSrwl3Shs2302HPx99fZbk5fZMfmDeTlZDF45HhPi4LeX1NjjHltRAbpbcfFhhgI75zI4W3rOLdHHNPGJvKLi6ouOYOMGhYirV2+iA7dz2Zfvj+Daom9B/cXPHGUuEolKiecPxGA+fN/s22rbwbNigL2nmLjmr8pKytlsI+GY7qTRiv8cp/8XcCfwC5gjpRyhxDiOSFExfPhp0CkEGI/8F+gWuimMwkKCqL3wKGsWb7IZydxOnTtyWOvfkC/oSM9LYpDK2ztodUIoiqVPiwuLACLGY0hmNSUZJdUXXIGJSYzBXasVrPJRER0LK36jcVskQztWHuZSW9V+NGVnryGntWJ4O4jOFl8WhWcyi2u133jaQt/3d+LCQoJpUefAR6VwxcQ3qwQExMTZVJSUr2PyykqY+b7n7Fn+2ZuuOdR/HXeNXHma7QIM9TquqiN1NxitiZbi3xnFJmJnvww+duWkr/JalHGtkzgxLGjaBrwBOEqTuYUs/14jt19Ukqe+W0nOj8Nj0/sVms/53SJdnvRE0fZeCTLlvZ51qpD/Hs0m9cv62WTt2+bcCICHbtv1h7M8KiVX5CXy5EDe+nuBXNdzmJwh8h6RcZVRgixUUpp98PwzqvRCZxz3mSmP/C0Tyr7k8eP8sNn75GT5bJpjnpRnxj8M6lw66SdPI45OwWh0RLYdZhtf2rKcdILvGvytqbqVnk52RzJKOR4dhHD6rDuA/Tur3BVH2JDTlv5A9tFUFhSytodB23bHJ1fkVJS6OFFV4HBIU1K2bsS770inYCprIy9O7Z4Wox6s3LxQj6a+RzFRYWeFgWof4ROZSrcOhULfvK3LSF/+1I0RmteoOi4eE5kO6/qkjPILqqu8EuKi7hqTB/ee2sm/lpB/7a1L+7xVndOBTHBBirmk7vGhZD65b188tJjtv2peSUOFUYpLDV7NGnagjlfMfeLDz0ngI/RpBX+tx+/xd1XTCA3O9PTotSLNcv/pF3nbsS29I70A42x8MFqTd5476PoDUYKD2ygYPtS/EKibVWXMvJLvKY8XonJTGFJdVn+XbuC4qIi0g3x9G0dXmfUkrcrfJ2fhvByl41WI2jTrQ8pO9eTm18AgNksSXegMIq9uQ53Mverj1i/YqlHZfAlmrTC7z9sNBaLhfUuriLjTPJystm+ab1XJYBqjIUPVrfOuAunct+zM4k0aNDFdsRSnM99z85kzKQpSFn/yBBXkV1DsrS1yxejNwYiWvSo050DEOlFK2xrIrZStM7Y8RORZcX8vPB0psYT2XW7dfI8qPCTDx/g2MF9DB7lPfeKt9OkFX7nnr2JiIqxFXrwBTas+AuL2ew1Cl+rEej9GqfwtRpBZJDOVnVp4NgLMOWcIr7zWbY2jigXd2BP4VssFtYsX0R4l/5EhwXSJa724hoBOm2jfyTdQXSQ3ubWmTBuDBp/Pf8s/cO2PyO/tM4nrxw7q5HdxZry+9pb7hVfoEkrfI1Gw4BzxrJh5TLKSn2jtN7xo4eIim1B17P6eFoUAKdVaqpsTV54oTVad96807HfhaXmWouFuwt7C6727dhCZtopTPF9GdohCk0di6kig7zfuoeqbh29wUjrswdzfOsqcivNYaTU8uQlpfSswv/rT9p37k5cfOu6GyuAJq7wAQaPHEdhfh7bNq3ztCgOcc0d9/PFH2vRaLzjq3GWpRoZWKn0YbdOhHZKJPmMydrjHrbyS0xmu+GFLVq1ZfQtT2Ls0J8htaRSqMDRcEZvoPIP8bTp9xB1/n0kHT4955VSy3eSX1Jz+UdXYzab0ekNDB83ySPj+yreoVVcSN/BI3jti5/plTjY06LUScWaCJ3OeyzExk7YVuCn1dgyRwohuPqZDynuOr5KCcHUvGLKGllbtTFkFdi3VoNCw8hpPZwe7VvWab1rNL6l8CvcOkvnz+XjZ+5BYwzlq/nLWDp/LmB98qqpzGNN8x3uQKvV8tLH33H17f/1mAy+SJNX+AZjAGcnDkbr511JrOzx8WvP8ej0K71qdbCzFD5UXeEpjyRhsVi4cfrtTBubyNL5c7FYPDt5ay8qJf1UCp9+/BGn0jIcmqwNNeoalIbCU+j8NKxdPM9WkjJ3wy8UHN3BWzNfsin9mtw6nnTnFBUWeGxsX6bJK3ywFhH54OWnOXpwn6dFqREpJauW/I5Gq/GqhFsGnfMukajyVMFL58/l0+fu5cQnt1OWnWJLs7B0/lySszzj1pFS2l1wtXLJQua89TS6snz6tKq7sIYvWfcVvP/q86dLUu5dTdZfn6CN78msN2cA1lQL9mLyPWXhl5YUc+XoPsyZ9a5HxvdlmoXC12i1/PTVR/zz5291N/YQh/fv5sSxw14XceCsSVsAvZ+WsAB/Zr05o1zBCEpO7MEvqi0lxUXMenMGBSWmGl0IriSvxESpqbo7adWyRfhHJDA88WyHavpGBPiewj9xPNn22lJitZy1AaGkpiSzdP5cTGZJWl7Vp5+84jKPrZ3YvH4VBXm5tO3kmhTCTZlmofAjo2Pp1iuRlUsWelqUGlm5eCFCCIaMPs/TolTB0MiQzDOJCtLb6qqa8zOQJQUYEqw5aSq2e8LKz7STHbMgP4+tG1Zh7DjAIXeOVisIMXq/6/BMzixJKXRGSk/uxy8ywfbkdSSjqgvlaKbnVoGvWfYnBmMAvQcM9ZgMvkqzUPgAw86dyIHd20k5dsTTothl5eIFdO/dn8joWE+LYkOrEQ5ZtfUhOvh0mgVZWgQaLVgsIDS27adyi91uPWbYyeez7u8lWEwmWvc5hzaRAXaOqkpEgM6r3HGOcmZJSmmxUHR4MwGdBtuevPKKTbY5jhKTmVO5nplrkVKyZtkiEoeOQqc31H2AogrNR+GPseb9XrnU+6x8i8XCuIsu5+Jrbva0KFXQ+zv/8gjU+3H7g4+jNxgB0BhDKDq0kaBOA7jx3kcBkBKOudGCNJktdicgt27dijYokvNGD3dIkfui/x6s1ck++uij0xtMJQitH7oYa/Woiievg2kFZOSXsD8132P5c/Zu30xG6km1uraBNBuF36JVG3oPGEppiXdlZgTrArEp193KOePrX17OlTgzQqcy066axn3PziSmRQKWwlzCRt6AvvNQZr05wxYZkpxdhMlNIZqZhaV2FVjLc2+k1fQPGdLRsVKb3la/tj5cffU0WsSfzt1k7DyUwG7D0cV1QggNS+fPJbeojH+PZpPiwWR3sfGtuO2hZ71urstXaDYKH+DVz+Yy7dZ7PS1GNdb9vZj8XPv51z2JMydsKxMdrGfMpCnWhGp6HZaiPAI6DyEtM8vmMzabpduyaNqLzikzm1lzMIM+HeIINtSdCC1Q79egMpDexFPP/s/25FW0fy2WslICuo3AYjHbvhdPExYRxZTrbiUkrO6IKUV1mpXCB6sPsCA/z9Ni2Eg7eYIn7riG377/wtOiVMNVCj/U6I/eX2OL1snbtIC8jb8S2GOUzWcMcCyr0C1rEuxN2D553x0c+mlmnVWtKqi8xsBXmX7DtTzwv9fQaLTIkgJOfHQzGp0RhKbK9+Ipjh3az+J5c7wmbbgv0uwU/hN3XM1z997kaTFsrCqfUxh+7vkelqQ6Bhf48MG60jYuxGDzDZsyj5H99xcYWvUETvuMi0rNpDmQorcxFJaaKCytOkFcUlzE5hWL0Ot09HSw0ldMiO8rfI1GcOVVVyGl1b9lLsqj+OhW9K16AKe/F0/x58/f8dpT//VKt6yv0Kg7WggRIYRYLITYV/7f7nOWEMIshNhc/ndmgXO30r5zdzavX+U1OfJXLF5A245dSGjbwdOiVMNVPnyA2FCDLSrHiqD05H4MbXoRFBLGtLGJjOvZgl7dOjF79myXyZGeV926/2fZUsylRQweM9GhVbN6fw0hDrh9fIGY4Erfi8VM0f71BHSxViir+n25Fykl/yz6jT4Dhyt3TiNorAn3CLBUStkJWErNxcmLpJS9y/88OjM5fNwkLGYzKxd7PlonKz2N7RvXMcwLrXtwnUsHIMTgz+0PnI7WASjYvYLgvpMoKswnNSUZKSUnjydzyy3TXab07T1B/DbvZzSGIKZOGu9QH03BnVNBZKCOW/77mPV7kRZkWTEafSD6wGBbFJUn2L9rGynHjjBi/AUek6Ep0FiFPxmocD5/AVzUyP5cTqfuZ5PQtgN/LfjJ06Kwcc3fWCwWr7yIhQC9k2Pwz+Saa662ReuAxJxzCm1wFNJQ1Y1SVFTI448/7vTxy8yWaqt6S0qK2bthObFnDSMhsva89xVE+Ug6ZEfQaARXXHkV9z0702rRa7QUH9pIUMf+vPzIXba8R+7mnz9/Q6PVMnSMdy1M9DUae0fHSilTyl+fBGpaNWQQQiQJIdYKIS6qrUMhxPTytklpaWmNFM9u/4w+/xK2Jq0h7eQJp/dfH8ZeMJXPF66hXaduHpXDHjo/1+f0iQsx2Iqi/LhyB8aAIMoyjhHcu/pNffToUaePn1lQyplzwvtP5hDU/2LGXXS5Q31oNcIn0ynURmz59/LN0o2ce+FUjG37ItokIqWskvfInRw5sJfeA4cREhbh1nGbGnUqfCHEEiHEdjt/kyu3k9ZwippCKtpIKROBq4A3hRA1OqyllB9JKROllInR0Y7FP9eXcRddxmOvvu8VvsD4Nu08LYJdXOm/ryBQ70dIee3XpFXLCQoJRaMPJKjXeNBWDXEUGo3T3Tpn5ocB2HiiiJgRVzH1fMfivCMCdWh8KDumI0QG6vDTWs9py7pVWEoLMXYcgPC3rmz1RMTOc+98wTNvzXLrmE2ROhW+lHKslLKnnb95wCkhRAuA8v+pNfRxvPz/QWA54NFyTrEtWzFywkVV/MfuZs6sd5nx0B2Yzd5RvPtMGlvW0FHiQgwsnT+XN55+gLSTx8n7dwEaQxCBXUdUaWcxm53qyzeZLdUUfkZGBkt//5U+LQMdnr+IakL++wo0GkFMsFW5p508Tv7WRRTtW0tA5yG2Nu6M2Km4R4wBgW4bs6nSWJfOr8B15a+vA+ad2UAIES6E0Je/jgKGAjsbOW6jyc3O4ruP/4/kwwfcPraUkoU/ziYz7RRarXfWPnVVSOaZxIbqK2XPhOJDm0j79RVC+l9Ura0zffnp+aXVUv5+/d33nJj7Iu20jkdwRfnw6traiC0PM42Oi6f01AHS57+OsWN/2353ReyUlZZy/YRBzPtGWffOoLF39UvAuUKIfcDY8vcIIRKFEJ+Ut+kGJAkhtgDLgJeklB5X+GVlpXz29gyW/Pqj28feu30zx48cZPSkKW4f21FcGaFTGb2ftpq1WLR/PX4RLTG06VWtvbN8+Sk51TNyrlj4E4bo1oweOtChPsID/d32JORuIgJ16Pw03Hjvo/jr9CAtmPIy0AZHojcY3Raxs2HlX5w8fozYlgluGa+p0yiFL6XMkFKOkVJ2Knf9ZJZvT5JS3lz+erWU8iwpZa/y/586Q/DGEhkdS++Bw/hr4U9urzC1ZP5c/P11XrnYqgJXJE6riZYJZ9zMFjMF25YS0v/iam1jWzbesiwxmaulU9i4fTc5h7fTf+xkh+sJV7g9miJCCGJCrCkw7v/f6/jpjRTu/JvYgZO579mZjHGTsbJo3hzCI6NJHDrKLeM1dZrdStvKjD7/ElKOHWHn5iS3jWk2mVj++y8MGnkuQSGOreL0BO60XGe88GK1+ZTcDb9g7JCIf+TphF56g5Hr73mUjEauvj2ZU1wtOufbb6xzA9dcfbXD/TSl+Ht7xJb/oI2ZNIWb//MIpSf3EdNzGKPPv8Qt4+dkZbBu+WJGT7oEP/+msbDN0zRrhT983CQMxgD++Plbt41ZWlLCeRdfyYSpjisWT+AuHz5Y4/GfffVtYlokIIQgICgYc85JZF4aMedMs1qbLRJsluWBtMbVMz2eXdWdU1BiYt+2TcR26Uu7tm0c6iM0wN9tbi9PERbgb6uHMHLiRWj9dRzbt81txU+WLfwZk6mMcZMdC5FV1I1vp/drJAGBQYyZNIWC/FyklG4pXmEMDOSm+5y/iMiZaDSg07rXFrjtxuvoN9q6AC0l+Qhb1q/iRGQ71ofG8MOGOwk1nrbwcovKSM0tJiak/i6V7MJSCkuqRkatOpBO1NRnuH+E4+6ihHDPRXi5iwq3TnJmEZHRsXy1dAtP/n6QNQczaBPp+oiZvoPP4Zb7n6R9l+4uH6u50KwVPsA9T73ssM+2sWSmpbJv11YSh47y2ugcsLpz3F25KTTAn9AAf3IKy2iR0IYWCW04mVPM6iPbWb4nlcm9qyrjvafyCQ/U4V/PH6YzyydapOSvnSfpFBNM93YtHepD56exuTuaOjHBBpIzrZ9ZdGQ4vVqFsWbfSab2S8DPxfdN6/adaN2+k0vHaG40a5cOYFP2qSnHXT55+/vc2Txx+9WcOn7MpeM0Fne6cyrTKvx0mb2S4iLW/PY1rcqOsWxPWrUC48VlZnaeyK1X/0Wl1Uvzbdh9hM2vXEl0+iaH+0kINza5xVY1EV7JrQNw6IcZHPz22Xp/9vXlj5++YWvSGpeO0Rxp9gofYO3yRVx9biK7tjp+09cXU1kZ8+d8Sd/BI2jZuq3LxnEGngo1jAnW26KDhBB8/f7r5G34mfwSE2sOZlRrn5ZXUq9SiIfSC6pN1n7z1ZeYC7IYkVg9BNQe/n4aWkXUXd+2qVDh1qmgW5dOFB/cxOJ121w2ZkF+Hu/NeJI/fnLf3FpzQSl8oFf/oRgDg/jl60/qbtxAVi5ZQPqpFC6+2rvq1trDUxa+RiNsVr5Ob+C8S65k2+qlxGrz+XPHSSyW6k9g+1LzyC2uXo/2TIpKzZzMrerOOZldwN6/f6JF51506tbDIRk7xwbV243k61R2X11w2bUIrYY1v82msNTkkvEWz/ueosICJl91o0v6b840ryu3BoyBgUy45Cr+WfQb6aknXTLGT199TMvW7RgwYqxL+ncmnlxMFB9uRFuex+WCK64DKTHsWURqXgkbDldfAWuxwNZjOXUqnz2n8qrVrf3i2x8xZZ9k2k13OCRbeKA/LUKb/mTtmYQF+NuevKJiW9B/1PnkbvmTVTud75o0m838MnsWXc/qQ5eevZ3ef3NHKfxyJl91I9Ji4ecvP3J637nZmWSmneLiq2922wRxY3Dnoqsz8ddqiA+zKtW4+NaMGH8hSX/MIcZgYsG2FJb8NtdWHKUiVW9xmZmkw1k1WvqpecWkn5E3p8RkZtXPnxEYHc/YCZPqlEujga5xIY0/QR9ECFFlzcG1N9+OLC3i5++/dvpYq5f+zvEjB5l6/W1O71uhFL6NFq3acM55k1k073tKS51bQi0kLILPF65h4tRpTu3XVXg6vrzy5O1lN95Bh649GdpSx4mcYj745idbcZTKqXpLTRY2Hski64wVtLnFZexKqVrDeOn8udxy9/2Ejr0NXXAky3//pU6Z2kQGEqhvvkFtlXP+dzmrD+fd9QLF7UfYzTjaGIoKC+jeuz/Dzq37R1hRf5TCr8TN9z3ORz8vR6dz3grKzLRUSkuK8fP3R6f3jVA+Vxc+qQujTmubKOzU/Wxe//IXJgzpgyUzmcDBV1ZJnVxSXMQrj97D0vlzMZslm45msf14Dqm5xRzJKGDjkSzKKkX4WDNzPojoPBKkJOvg1jrzuwcZ/GjnhrhzbyY8QEflh9Mbrr0GrT6QtXYm0xvDuIsu582vf/XqsGVfRin8SsS0TCA8KhopJWWl1WudNoS3nnuIOy4dh+VMB7KXIoT7F13Zo/UZkTDZGWmc+m0m/mFxBPeeWGWfxWK2KW0prakTtibnsO9UPmZz1YneWW/OQEa0JmfN9+Ss+R6oPb+7RgM940ObTRhmTWg1gvBKhV4iAnVE5e7l86duoaSkuJYjHUNKyeq//sRisbh9DUhzwvN3tpdhKivjgRsuYdZbLza6r61Ja1j91x+MmnixT/juwT2VrhwhLEBHaMDp1bX/9/yjlJ06QMHe1YQOvQKhr2px11WUY+l8q+8/NSUZWVpE0aFNFO1bZ9tfU373jtHBBDVjV05lzizl2C0uiNz9G/ns4w8b3ffKxQt4+u7rWLF4fqP7UtSMb2ghN+Ln70+LhDbMmz2Lk8cbnorXYrHw4SvPEBXbginX3epECV2Lp/33lWkTedrKn3bbvUgge/EHaAxBhA6aWq19TUq7osBKakoy2tA4ytKP4B/dlsoF2uzld48I0tEqovlF5dRE5Bm5/y+bfD4B7fvx6+f/R3ZmeoP7LS0tYdZbM2jToTPDxnpvBtmmgFL4drjurofQ+ml554XHGrz6dtEv37F3xxZu/M+jGIy+s1DHG9w5FUQH6QnQW3+AOnY7i/MvvQZzYTa5a38kJHEy2uCqJTBrKspRucCKLMnHP6YdJSf22Pbby+/u76ehe4sQr3ja8RYCdH62kFmwGgejr3+AsuJCPnmj4SUPv//kHZIPH+DWB59RvnsX4z13txcRHdeSG+55lHV/L2H579WKeDnE2r+XcFbiIMZcUN0S9Wa8ycIXQlRJ0nXjfx4lJDQMw6EVSLOJ8DGnF7HVVpSjwvIXugAsxfnoW3aDMqvfuXIWztPjwtnxoV71WXgLwWe4t84f3p+QxMn8+dNs9mz7t979JR8+wLcfv83ICZPpP3y0s8RU1IByTtbA5Gk3sWzhz/z67WeMnDC53pbeU298QkFers/47ivQeThC50ziQgzsT83nj19+YNabM8jJyqS4qIizcnaR1mUoBe0TCS46yY33PlpjUY7ouHhSU5IJHXI5GkMQOau+AazKfvaS6rUQusQFEx7YNEsXNpYggx/ZhafXO3SIDqTLpJsp6NiNzg1YKFVUWECrdh257eHnnCiloia86+72IrRaLU+8/hHPv/91vZT9/Dlfkn4qBY1GQ3BomOsEdBGeSqtQE1qNYOPSX20+eLBO0G6bM5MgUUL3G17k09/XMWbSFNvEbOVFWQBTr78NQ2Q8IYkXgsWCOS+jxieC9tGBJIT7jgvO3QTqqtqIQghGdI2noPUQTuYWc/zIIUxldae6kFIipaRT97P5YO4SIqNjXSWyohKNuruFEJcKIXYIISxCiMRa2p0nhNgjhNgvhHikMWO6k9iWrQgMCqa0pJgv332V0jrCz+Z9M4u3nn2In12Yk8fVeJMPv4I3X3rO5oOvoKQgjz1vXcfx3f8yJ+lYlYnZyouy5n0zi5+//piQmHhAkLvuB7tuHICECCPto4PceGa+R7ChulNgcIdINAIWJe3mzsvH88YzD2A21ZzqQkrJrLdm8P5LT7mtDoXCSmNdOtuBS4Aa47KEEFrgXeBcIBnYIIT41RsKmTvKv+tW8vX7r7N1wxoeefldomJbVNlfVlrKl+/N5LuP32bQyHFcf/fDHpK08Xij3zr5mP2cLaaifNJ/eJqFOXfif2pX9R+F4iLem/EkfjodUaPu4ZyucVy7eqvdvmJDDHSJDXa67E0Ne6uNQ43+nJ0Qxpa0fC6+5ha+fu81crMyefild6qV8SwuKuSDV55hwZwvmTj1aqXw3Uxji5jvklLuqaPZAGC/lPKglLIU+A6Y3Jhx3c3AEWN5aMb/sXvbv9x04Qg+ffNFjuy3nnZWehq3TRnDdx+/zXmXXMkzb83CX+e7/l9Pr7K1R+vWre1uj4xpQZeevciY/xpZp46hDYur1sZiMTPgrncIad29WhGVCoINfnRvqSJyHMFfq7FrFAzrGEVusYmzL7iZe558ifUrlnLdhMEsmPMVYE2K9uPnHzD94lEsmPMll914J/95+hWfm+PyddzxaccDlU205PJtPsXYC6by0c/LOLvfIObMepfvP30HgJCwcIJCQvnfu19y///eQOvnu/PgWo3AzwtdOi+88AIBAVX96nqDkVvuf4LXPpvLNfc8jikjGV1sB/zOUPrhvc7lmDaWE3+8zx0XDK6WQsHfT0OvVmFom/lK2voQZMetc1Z8KKFGf1buT+eCK67n3TmL6NitJ7u3WyN3hBB8/NpzhEdG8/KnP3DL/U8qZe8B6tROQoglQHXTCR6XUjYsZrH28aYD06Fmy85TtGzdlv+99xVZGWm2hSZaPz/emt00Vgd6o3UPMG2aNencI48+xvHkY0THxVeJyrn21rsxRMaz4IhE6Ayk/vAMZRnH0Md3J3js7RQf20HupgXklqdgAGzHdm8R4pVuLG8mSK8lvWo+OrQaweD2kSzaeZLswlI6duvJy5/MsU3gajQaPluw2uuL/zR1hDPK+gkhlgMPSCmrxbgJIQYDz0gpx5e/fxRASlnnSo3ExESZlFQ9bK4ucorK2HCoeu50Re2EB/rTr02Ep8Wolc3HsqulOq7gh19+44+0ENAZKctIxj8yAVPmCU5+/SCW4tMaqiIcs1VEAF3ilN++viRnFbL7jAykACdzi3nil+1M6RvPhJ4t7BypcJTBHSIbnJ1VCLFRSmk3iMYd/ocNQCchRDvgOHAFcJUbxlXUE08WPnGUTjFBZOSXVClVuHT+XGa9OYO0k8eJbtMFOg6DiNYU7l5B/pY/qyh7sC7E0vtr6BDdvDNgNhRjDU9EcSEGOsUEsWJfOuN7xKFRcyJeR6MUvhDiYuD/gGhggRBis5RyvBCiJfCJlHKilNIkhLgL+BPQArOklDsaLbnC6Xjboit7BOr9aBMZwOF0ay3binDMigid1MO74fDuWvuIjounU0ywV85X+AJGXc2GwcjO0Xy88hA7T+TSMz60xnYKz9DYKJ2fpZQJUkq9lDK2wm0jpTwhpZxYqd1CKWVnKWUHKeULjRVa4Rq81Yd/Ju2igmx+98p5chxBbzBy10NPEhfqG7UJvBFDLU+C/dqEE2Lw4689qW6USOEovnGHK9yCL1j4YJ0g7BxrXSBVU4ZMe4SEhXPfszO559YbXCVas0CjETWWwfTTahjROZptyTlOr4alaDy+cYcr3IIv+PAriAkxEGL0rzFDZnBoODEtEhBCENMigUdefpe5q3Yxbdo0Qo3+do9ROE5NfnyAczpHoxGC5crK9zp8N2hc4XR8xcKvoEN0IDfe+2gVHz5Y3TZ3PvZ8tdQJQlhz5Sgaj9WlZj9nTniAjj6tw1ixP50Le7f0KUOiqeNbd7jCpfiKD7+CyCA9l11xJfc9O7OKNW8vTw5AXKiBAJ2ycZxBbRO3AKO7xlBYamadCo/2KtTVrwCstVv9fTBqpWtcCOMunFpjauQKhID2USoxmrOoa7Fap5ggEsKNLNudyvCOUSpthZfge3e4wiX46mO3Uad1yE0TH26s0ypVOE5tPnywplIY3SWGY1lF7E/Nd5NUirpQCl8B+J7/vjKtIwIID6x5ItZPK5R172TqUvgAA9tFEKDTqhBNL8J373KFU/E1/31lhBD0aBmKn9a+26B9VJBP/6B5IwZ/DXV5afT+WoZ2jGLTkWyyC0vdI5iiVtRdoAB828IHq0/5rPjQakooIkhHqwijZ4RqwgghHLpmRnaOxiIlf+9Nc4NUirrw7btc4TR81YdfmcggPd1bhqAtt/QDdFp6qDz3LsORayY2xEDP+FD+2ZeOyWxxg1SK2lAKXwH4voVfQYtQI8M6RpHYNpzBHSKbxA+Zt+KoG3B01xhyisrYeDTLxRIp6qJp3OWKRuPLPvwz8ddqCAvQKcvexdSUXuFMerQMISZYz1+71eStp2k6d7miUTQlha9wD44+PWmEYFSXGA6kFXAko8DFUilqQ93lCqDpuHQU7qM+RsLQjpHo/DQs26Mmbz2JussVAOh8cJWtwrPUR+EH6PwY3D6SdYcyyC82uVAqRW2ou1yBzk+j/N2KeqOvZy3gUV2iKTNLVuxXVr6nUApfodw5igZR33mfhPAAusUFs3RXqgrR9BDqTlcoha9oEP5aDVpN/Z4Mx/eII7uojHWHVRZNT6DudIXy3ysaTH2t/B4tQ4gPM7Joxylk5Ur0CrfQqDtdCHGpEGKHEMIihEispd1hIcQ2IcRmIURSY8ZUOB8VkqloKI7G4lcghGBcj1iOZxex40Sui6RS1ERj7/TtwCXAPw60HSWl7C2lrPGHQeEZ1GpURUNpyLUzsG0EYUZ//txx0gUSKWqjUQpfSrlLSrnHWcIoPIPy4SsaSkOeDv20GsZ0i2HXyTy1EMvNuKvilQQWCSEk8KGU8qOaGgohpgPTy9/mCyEa+oMSBaQ38Fhvo6mcS1M5D1Dn4hRuftmp3anvxEqbmnbUqfCFEEuAODu7HpdSznNQgGFSyuNCiBhgsRBit5TSrhuo/Megxh8ERxFCJDUV91FTOZemch6gzsUbaSrnAa47lzoVvpRybGMHkVIeL/+fKoT4GRiAY35/hUKhUDgJlztvhRCBQojgitfAOKyTvQqFQqFwI40Ny7xYCJEMDAYWCCH+LN/eUgixsLxZLLBSCLEFWA8skFL+0ZhxHaTRbiEvoqmcS1M5D1Dn4o00lfMAF52LUIsfFAqFonmg4vEUCoWimaAUvkKhUDQTmozCb0ppHupxLucJIfYIIfYLIR5xp4yOIISIEEIsFkLsK/8fXkM7c/n3sVkI8au75ayNuj5jIYReCPF9+f51Qoi2HhCzThw4j+uFEGmVvoebPSGnIwghZgkhUoUQdoM/hJW3y891qxCir7tldAQHzmOkECKn0nfyVKMHlVI2iT+gG9AFWA4k1tLuMBDlaXkbey6AFjgAtAd0wBagu6dlP0PGV4BHyl8/ArxcQ7t8T8va0M8YuAP4oPz1FcD3npa7gedxPfCOp2V18HxGAH2B7TXsnwj8DghgELDO0zI38DxGAvOdOWaTsfBlE0rz4OC5DAD2SykPSilLge+Aya6Xrl5MBr4of/0FcJHnRGkQjnzGlc/xR2CM8L5qMr5wrTiMtC7arC2/8mTgS2llLRAmhGjhHukcx4HzcDpNRuHXg4o0DxvL0zj4KvHAsUrvk8u3eROxUsqU8tcnsYbo2sMghEgSQqwVQlzkHtEcwpHP2NZGSmkCcoBIt0jnOI5eK1PKXSA/CiFauUc0l+AL94ajDBZCbBFC/C6E6NHYztyVS8cpuDvNgytx0rl4nNrOo/IbKaUsz6Vkjzbl30l74C8hxDYp5QFny6qold+Ab6WUJUKIW7E+tYz2sEzNnU1Y7418IcRE4BegU2M69CmFL5tQmgcnnMtxoLIVllC+za3Udh5CiFNCiBZSypTyR+rUGvqo+E4OCiGWA32w+pw9jSOfcUWbZCGEHxAKZLhHPIep8zyklJVl/gTr/Iuv4hX3RmORUuZWer1QCPGeECJKStngBHHNyqXTxNI8bAA6CSHaCSF0WCcMvSrCBas815W/vg6o9uQihAgXQujLX0cBQ4GdbpOwdhz5jCuf41TgL1k+4+ZF1HkeZ/i4LwR2uVE+Z/MrcG15tM4gIKeSa9FnEELEVcwHCSEGYNXXjTMmPD1T7cQZ74ux+upKgFPAn+XbWwILy1+3xxqhsAXYgdV94nHZG3Iu5e8nAnuxWsNedy5YfdlLgX3AEiCifHsi8En56yHAtvLvZBtwk6flPuMcqn3GwHPAheWvDcAPwH6sqUPae1rmBp7HjPJ7YguwDOjqaZlrOZdvgRSgrPw+uQm4DbitfL8A3i0/123UErXn5edxV6XvZC0wpLFjqtQKCoVC0UxoVi4dhUKhaM4oha9QKBTNBKXwFQqFopmgFL5CoVA0E5TCVygUimaCUvgKhULRTFAKX6FQKJoJ/w/Sk6A7cIDZygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_test, m, label='Expected value');\n",
    "plt.fill_between(x_test.flatten(), m + 2 * s, m - 2 * s, alpha = 0.3, label='Uncertainty')\n",
    "\n",
    "plt.scatter(x, y, marker='o', c='k')\n",
    "plt.plot(x_test, f_test, 'k--')\n",
    "\n",
    "plt.ylim(-1.5, 2.5)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you think something can be improved in this article (and I'm sure it can) or if I missed other important aspects of PyMC4 please let me know."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
